MACHINE DESIGN 


PART I. 


American 

School of Correspondence 

(Chartered by the Commonwealth of Massachusetts .).• 

Copyright 1900 

BY 

American School of Correspondence. 


BOSTON, MASS., 
U. S. A. 





MACHINE DESIGN 


PART I. 


INSTRUCTION PAPER 


American 

r» 

School of Correspondence 

(Chartered, by the Commonwealth of Massachusetts.) 


Copyright 1900 

BY 

American School of Correspondence 



BOSTON, MASS., 
U. S. A. 


TWO COPIES RECEIVED, 
Library of CeBgpefi^ 
Office o f tfc« 

APR 2 61800 

•“■sl'tor of Copyrights, 



TJ£50 

,Asz 


/ 



"A 





SECOND COPY, 






ffVZ- 

(? 00 ’ 



MACHINE DESIGN. 


Machine design treats of the design and construction of 
machines and their various parts. 

A machine is a combination of movable parts, arranged on a 
supporting frame, and placed between the source of power and the 
work. 

The object of a machine is to transform the energy supplied 
at the point where the machine receives its motion, into work at 
the point where the resistance is overcome. 

The various parts may be arranged to change the direction or 
velocity of the power or to overcome great resistance with small 
force. For instance, a steam engine changes rectilinear to circular 
motion while a planer changes circular to rectilinear. A lathe 
is a familiar example of the change in velocity. Hydraulic presses 
and testing machines illustrate the overcoming of a great resistance 
by a small force. 

A machine cannot move of itself nor create power. According 
to the law of the conservation of energy, no increase of power can 
be obtained from any machine. If a machine were frictionless, 
the product of the force exerted at the driving point and the 
velocity of the driving point would equal the product of the 
resistance and the distance through which the resistance is over¬ 
come in the same time. 

The operation of machines depends upon two conditions ; the 
transmission of certain forces and the production of definite result¬ 
ant motions. 

In designing machinery both of these conditions must be con¬ 
sidered. The machine must be constructed so that each part will 
bear the strains placed on it and also have the proper relative 
motions. 



4 


MACHINE DESIGN. 


The nature of these relative movements is independent both 
of the power transmitted and of the dimensions of the parts. We 
see that this is true ; for in the model of a machine, the dimensions 
of the parts may vary considerably from those requisite for strength. 
At the same time, the relative motions of the parts of a model 
which may be worked by hand, are the same as those of the larger 
machine which perhaps transmits 1000 H. P. 

Pure riechanism treats of the motion and form of parts of 
machines and the manner of supporting them. 

Constructive Mechanism treats of the calculation of the 
forces acting on these parts. It involves the selection of materials, 
and the calculation of the dimensions for requisite strength and 
stiffness. 

A riechanism is a portion of a machine where two or more 
parts are so arranged and connected that the motion of one com¬ 
pels a definite motion of others. 

Machines are made up of trains of mechanisms. The sewing 
machine, watch and printing press are examples. 

notion and rest are relative terms. If we consider some 
point or body as fixed, motion may be either relative or absolute. 
For this work the earth is assumed to be fixed and motion referred 
to it absolute. 

A point moving in space follows a line, either curved or straight 
which is called its path. 

Direction, like motion, is relative to continuous motion. If 
a point continues to move indefinitely in the same direction, it is 
said to have continuous motion. In this case, the path must be a 
closed curve. A shaft turning on its bearings or the crank-pin of 
an engine, is an example of this motion. 

Intermittent notion. When a part of a machine has motion 
in alternate directions and definite periods of rest, it has intermit¬ 
tent motion. 

Reciprocating Motion, If a point travels in the same path, 
alternately in opposite directions, its motion is said to be recipro¬ 
cating. If the motion is reciprocating and also ciroular, it is called 

vibration. 

Velocity. The ratio of space to the time is called linear vel¬ 
ocity, if the path of the moving body is a straight line. If the 



MACHINE DESIGN. 


5 


path of the body is a curve the ratio of space to time is called 
angular velocity. 

Velocity may be uniform or variable according as the spaces 
traversed in equal times are equal or unequal. 

Velocity = - -P a _ e 
Time 

Space — Time X Velocity. 

The unit of space is usually one foot; the unit of time, one 
second. Hence velocity is expressed in feet per second. 

Angular velocity is measured by the number of units of 
angular space passed over in a unit of time. Angular space is 
measured by circular measure of the ratio of the arc to the radius. 
The unit angle is the angle subtended by an arc equal in length to 
the radius. Angular velocity may be expressed in number of 
revolutions in a unit of time; one revolution is represented by 2 7 r 
in circular measure. 

Linear velocity 


Angular velocity = 
Linear velocity 


Radius 

= Angular velocity X Radius. 


Suppose we wish to find the linear velocity of some point on 
the periphery of a fly-wheel. Evidently the point will travel, 
during one revolution, a distance equal to the circumference 
of a circle of the given radius. The circumference is, from 
geometry, tt d or 2 it r. Let n be the number of revolutions per 
minute, then the linear velocity is 2 it r n. 

A fly-wheel is 20 feet in diameter and revolves at the rate of 
50 revolutions per minute. Find the linear velocity of a point on 
the periphery. 

Linear velocity — 2 tt r n — 2 X 3.1416 X 10 X 50 
— 3141.6 feet per minute. 

How far from the centre of this wheel must a point be tr 
have a velocity of 20 feet per second ? 

y 

V = 2 7r r n, or r — 

2 7 rn 


Then, r = 


1200 


2 X 3.1416 X 50 
= 3.82 feet. Ans. 






6 


MACHINE DESIGN. 


EXAMPLES FOR PRACTICE. 

1. A wheel 3 feet in diameter makes 25 revolutions per 

minute. What is the linear velocity of a point on the circumfer¬ 
ence ? Ans. 235.62 feet per minute 

2. A wheel makes 300 revolutions per minute. How far 

from the center must a point be to have a linear velocity of 2827.44 
feet per minute ? Ans. IT feet. 

3. Find the linear velocity of a fly-wheel when the angular 

velocity is 188.5 revolutions per minute, the wheel being 10 feet 
in diameter. Ans. 942.5 feet per minute. 

Revolution. A point revolves about an axis when it describes 
a circle the center of which lies within, and its plane of rotation is 
perpendicular to, the axis. If the axis passes through the body, 
as in the case of a wheel, the motion is called both rotation and 
revolution. 

A body, like the earth for instance, may rotate about its own 
axis and also revolve in an orbit about another axis. 

Cycle of JTotions- In case the parts of a mechanism go 
through a series of motions which are repeated, each time the 
order of the motion of the several parts being the same, the series 
is called a cycle of motions. In the steam engine every revolu¬ 
tion is a cycle because each series of motions is repeated for every 
revolution. Two revolutions of the crank are necessary for one 
cycle in some types of the gas engine. 

The part or piece of mechanism which causes motion, or to 
which the power is applied is called the driver and the part whose 
motion is caused by the movement of the driver is the driven or 
follower. 

Frame. The structure which supports or holds in position 
the moving parts and regulates the path of motion is called the 
frame. The motions are often referred to the frame, as it is 
usually fixed, that is, without motion. An exception to this is the 
locomotive frame. 

Transmission. One object cannot move another unless the 
two are in contact or are connected by some body that is capable 
of communicating motion from one to the other. The above state- 



MACHINE DESIGN. 


7 


ment does not take into account the action of natural forces, such 
as gravity, magnetism, etc. 

Motion transmitted by contact is seen in friction gearing, gear 
wheels, etc. Belts, rope gearing, levers, links, etc., are examples 
of motion by intermediate connection. Connectors are either rigid 
or flexible. 

notion. Mechanism may be used to change the motion of 
the follower from that of the driver. It may differ in direction,, 
kind, or velocity. 

Work is the overcoming of resistance through distance. It 
is the product of the resistance and the space through which it is- 
overcome. If a body is lifted from the earth, against the attrac¬ 
tion of gravity, the resistance is the weight of the body and the 
distance is the height to which the body is raised*. The work 
done is equal to the weight of the body multiplied by the distance. 

The Unit of Work is the foot-pound, that is, the amount of 
work done in lifting one pound through one foot. If F equals 
the force or weight and S equals the space or distance through 
which F is moved, then work = F X S. S = velocity multi¬ 
plied by time = V X T. Then if we raise 5 pounds to a height 
of 20 feet we do 5 X 20 = 100 foot-pounds of work. 

Energy is the capacity for doing work. There are two kinds? 
of energy, potential and kinetic. 

Potential Energy is energy of position; water stored in a 
reservoir for example. The water is capable of doing work by 
means of a water wheel. Potential energy is measured in foot¬ 
pounds, that is, it is the weight of the body multiplied by the dis¬ 
tance through which it is capable of acting. 

Potential energy may also exist as stored heat or chemical 
energy, as in fuel, gunpowder or electric energy. 

Kinetic or Actual Energy is the energy of a moving body.. 
The energy in a moving body is the work which it is capable of: 
performing against a resistance before it is brought to rest. It is- 
equal to the work required to bring it from rest to its actual 
velocity. Kinetic energy is measured as the product of the weight 
of the body and the height through which it must fall to acquire 
the actual velocity. From the laws of falling bodies this height 



8 


MACHINE DESIGN. 


equals the square of the velocity divided by twice the value of 
the earth’s attraction. Then 


A == 


and energy. 


% 


E = wh = 


2 g 


The weight of a body divided by g is called the mass, i. e ., 


m = 


w 

V' 


then substituting m for — in the equation 
9 


1 ^ W V • i I t > 

E = , it becomes E 

*9 


mv 2 


Energy is the capacity of doing work. The units of work 
and energy are the same; then 


F S = ivh 



mv 2 


Power is the rate of performing work. It is equal to the 
work done divided by the time and is expressed as foot-pounds per 
minute or per second. Thus horse-power is a measure of power, 
being equal to 33,000 foot-pounds per minute or 550 foot-pounds 
per second. 


Power — 


FS 


MATERIALS, 

The principal materials used in the construction of machinery 
are cast and wrought iron, copper, wood, brass and other alloys. 
The properties and processes of manufacture for iron and steel 
have been described in Metallurgy. 

CAST IRON. 

Cast iron is used to a considerable extent in the construction 
of machines. For the heavy massive parts, the frames of lathes, 
steam-engines, planers, etc., for example, it is the best, material. 
It is not suitable for parts requiring strength, elasticity or those 





MACHINE DESIGN. 


9 


subjected to shocks. For this reason piston-rods, connecting-rods, 
shafts, etc., are usually made of steel or wrought iron. 

Many complicated shapes that cannot be forged are readily 
cast. The ease with which parts may be given the desired shape 
makes cast iron valuable. 

Cast iron contains 3 to per cent, of carbon with a little 
silicon. The hard and white varieties are used in the manufac¬ 
ture of wrought iron. The gray irons are used in the foundry. 

Cast iron is made into the desired forms by melting it in a 
cupola and pouring into moulds. The moulds are made in sand 
or loam from patterns of pine wood. Patterns are made a little 
larger than the required casting because iron in solidifying con¬ 
tracts about i inch per foot in each direction. This contraction 
is called shrinkage. In making a pattern a shrinkage rule is used 
which is about ^ inch longer per foot than the standard. 

Castings are likely to be put into a state of internal stress 
because of contraction when cooling. If some parts of the casting 
contract more than others, the casting may become twisted. Thin 
parts of the castings solidify first. The contraction of the fluid 
parts strains the portions already set and their resistance to 
deformation causes stresses to be set up in the parts which are 
solidifying. 

For example, the form shown in Fig. 1 has a rigid flange 


Fig. l. Fig. 2. 

surrounding the inner part. If the contraction of the cross piece 
takes place more slowly than the rim, it is likely to fracture. In 
a thick cylinder, as shown in section in Fig. 2, the outer portions 
solidify and begin the contraction. The contraction of the inner 
induces pressure in the outer portion, which being rigid causes a 
resistance to contraction of the inner layers and puts them in ten- 

















10 


MACHINE DESIGN. 


sion. A cylinder so constructed is not strong to resist bursting 
pressure. If the cylinder is cast while water circulates through 
the core, the reverse distribution of initial strains is set up. This 
insures a stronger cylinder because the inner layers are in a state 
of compression and the outer portions are in tension. 

The arms of pulleys may be broken by tension if the rim is 
thin and rigid. If the arms set first the rim may break near 
them. To have successful castings, the designer must carefully 
consider the dimensions of the various parts. 

On account of these initial strains, that cannot be calculated, 
cast iron is unreliable. Cast iron structures usually have exces¬ 
sive dimensions to insure safety. 

In cooling, the crystals of cast iron arrange themselves per¬ 



pendicularly to the surfaces from which heat radiates. For 
this reason all corners should be well rounded as shown in 
Fig. 3, so that the arrangement of the crystals will make the 
castings strong. 

Chilled Castings. If castings are cooled rapidly during 
solidification, the graphite is prevented from separating from the 
iron. This causes the iron to become harder. In order to chill 
the cast iron, the mould is made of or lined with this same mate¬ 
rial. The mould which is lined with loam for protection, is a 
good conductor of heat and the molten cast iron is cooled or chilled 
during solidification. 













































































































MACHINE DESIGN. 


11 


The chilling usually extends to a depth of ^ to | of an inch 
from the surface ; the interior remaining soft. 

Malleable Cast Iron. Malleable cast iron is made by sur¬ 
rounding castings with oxide of iron, powdered red hematite or 
peroxide of manganese; keeping them at a high temperature for 
a considerable time according to the size of the casting. The 
elimination of carbon converts the cast iron into a crude form of 
wrought iron. Malleable castings will stand blows better than 
ordinary castings. 

Cast iron is stronger than wrought iron when under press¬ 
ure ; but it is much weaker under tension and impact. 

WROUGHT IRON. 

Wrought iron is made from cast iron by eliminating part of 
the carbon. It is strong and tough and can easily be welded. 
For these reasons it is used for parts of machines and structures 
requiring strength and of simple form. Wrought iron parts are 
shaped by forging and finished in the machine shop; steam ham¬ 
mers being used on the heavy portions. 

Wrought iron is rolled into plates, round and square bars, 
angle, tee, channel, I beam sections, etc. Large wrought iron 
structures are built up of bars or plates riveted or bolted together. 

Wrought iron that has been rolled when cold has a greater 
tensile strength than before rolling; but its ductility and tough¬ 
ness is reduced. Annealing, or heating the iron to a red heat and 
allowing it to cool slowly, restores it to the original condition. 

Compression of iron when cold increases its strength but 
reduces its ductility and toughness; annealing reduces strength 
and increases toughness and ductility. If the iron is rolled or 
hammered when hot, compression and annealing are carried on at 
the same time. 

Wrought iron is used for piston-rods, shafts, connecting-rods, 
bolts, nuts, chains, etc. 

STEEL. 

Steel is far the most useful material used in machine design. 
Its properties depend upon the percentage of combined carbon, 
silicon, manganese, phosphorus, etc. Steel contains from .15 to 
1.5 per cent, of carbon. 




12 


MACHINE DESIGN. 


Formerly it was difficult to get sound castings, but by the use 
of silicon, aluminum and other elements and prolonged annealing, 
the internal stresses are destroyed. 

Steel can be welded, but greater care is necessary than in the 
welding of wrought iron. 

Tempering greatly increases the usefulness of steel, since it 
becomes hard if heated and cooled suddenly. With good steel 
almost any desired hardness may be obtained. The steel is heated 
to the temperature indicated by the color of the oxide which forms 
r.tits surface and is then quenched in oil or water. Hardness 
makes it suitable for cutting tools. When tempered it is hard, 
strong, has high elastic limit and little ductility. 

COPPER. 

Copper is a reddish metal of great ductility and malleability. 
It is usually rolled or hammered into shape because it doesn’t cast 
well. Copper can be welded, but as it requires considerable care 
to make a good joint, pieces are more often joined by brazing. It 
can be drawn into wire. The tensile strength of cast copper is 
about 20,000 pounds per square inch; of forged copper about 30,000 
pounds per square inch. 

Hammering, rolling and wire-drawing increases the tensile 
strength, but makes it hard and brittle. It can be made soft and 
tough by annealing. It is expensive and is used for wire, fittings 
and tubing. Its strength is less than that of wrought iron and 
decreases rapidly with rise of temperature. 


ALUniNUM. 

Aluminum is a soft, ductile, malleable metal of bluish white 
color. It is very‘light; next to magnesium the lightest of the 
useful metals. Its strength is about one-third that of wrought 
iron. Aluminum casts well, the shrinkage being about the same 
as brass. The readiness with which aluminum unites with other 
metals makes it valuable for alloys. It can be electrically welded 
but doesn’t solder well. 



MACHINE DESIGN. 


13 


BRONZE. 

Bronze, or gun-metal, is an alloy of copper and tin ; about 90 
parts copper and 10 parts tin. It makes good castings. Bronze 
is harder and less malleable than copper. Copper-tin alloys are 
used for bearings because it is softer and wears faster than wrought 
iron or steel shafts. 

The hardness of bronze depends upon the proportion of tin ; 
to increase hardness increase the amount of tin. An alloy of 92 
parts copper and 3 parts tin is a soft bronze used for gear wheels. 

Phosphor-bronze is made by mixing 2 or 3 per cent, of phos¬ 
phorus with ordinary bronze. Soft phosphor-bronze has a tensile 
strength of about 45,000 pounds per square inch; harder varieties 
have about 65,000 pounds and hard unarinealed wire has about 
150,000 pounds. It is used for pump-rods, propellor-blades, etc. 

Manganese bronze, called white bronze, is an alloy of ordinary 
bronze and ferro-manganese. Like phosphor-bronze it is used in 
marine work, because it resists the corroding action of sea-water. 
Manganese bronze is equal in tensile strength and toughness to 
mild steel and can be easily forged. 

BRASS. 

The alloy of copper and zinc is called brass ; sometimes tin 
and a little lead are added. For bearings it has about 60 per cent, 
copper, 10 per cent, zinc and 30 per cent, tin and lead. Naval 
brass has 62 per cent, copper, 1 per cent, tin and 37 per cent. zinc. 
Red brass consists of about 37 per cent, copper and for the rest 
about equal parts of tin, zinc and lead. Brass is used for bear¬ 
ings, wire, fittings and ornamental work. Its tensile strength is- 
about 23,000 pounds per square inch. 

FUSIBLE ALLOYS. 

Fusible alloys are made of tin, lead and bismuth. The melt¬ 
ing point varies with the percentages of the various constituents. 
If made of 2 parts lead and 1 part tin, it melts at 475° F.; if 1 
part lead, 1 part tin and 4 parts bismuth, the melting point is 
about 200° F. An alloy of 1 part cadmium, 4 parts bismuth, 1 
part tin and 2 parts lead melts at 165° F. 



14 


MACHINE DESIGN. 


BEARING ALLOYS. 

The principal constituents of bearing alloys are copper, tin, 
lead, zinc, antimony and aluminum. The bronzes contain a 
large per cent, of copper. A good bearing alloy is made of cop¬ 
per, 77 parts by weight, tin 3 parts and lead 15 parts. 

Babbit metals have various proportions ; hard babbit haviijg 
about 89 per cent, tin, 4 per cent, copper and 7 per cent, antimony. 

There are many other alloys containing the metals in varying 
proportions according to the intended use. 

WOOD. 

Wood is but little used in machine construction. Soft woods 
like pine are used for patterns; hard varieties, oak and lignum-vitae 
for examples, are used for bearings. Sometimes levers are made 
of wood and the pulleys of some lathes are constructed of the same 
material. The cogs of mortise wheels are often made of beech or 
horn-beam. 


SHOP PROCESSES. 

In designing machinery it is necessary that the parts may be 
easily made. A finely finished pattern is of no value if it cannot 
be taken from the mould. Complicated castings and forgings 
should be used only when absolutely necessary. Simple designs 
are usually the best. 

For casting, patterns or models are made from wood in the 
pattern shop. The pattern maker has to consider and make allow¬ 
ance for shrinkage in casting, for turning, boring and finishing. 
He arranges the patterns in such manner that the moulding, cast¬ 
ing and finishing may be most cheaply done. Some parts can be 
moulded only by the use of cores. Parts to be finished by cutting 
tools must be so placed that they will not be unsound by reason of 
blow T holes. The founder follows the specifications of the draw¬ 
ings ; mixing the pig iron in different proportions so as to get the 
required strength and softness. 

Forging is the operation of shaping wrought iron or steel 
without melting. These materials become plastic without fusing. 
The pieces are hammered or rolled into shape. If the work fo 




MACHINE DESIGN. 


15 


light the smithing is done by hand; but when large forgings are 
made, steam hammers are used. When the pieces are very large, 
great skill is required to arrange the operation so that the result 
shall be a homogeneous sound piece. 

Fitting, finishing, boring and turning are the operations of 
cutting the rough products of the foundry and forge to accurate 
dimensions. Fitting, boring and turning are done by steel cutting 
tools which shape the metal when cold. Cutting operations in¬ 
clude chipping and filling, drilling, turning, planing, shaping and 
milling. 

Conical surfaces, screws and nuts can be made in the lathe. 

STRAINS IN HACHINES. 

There are forces acting on the several parts of a machine 
which will cause them to give way if they are not sufficiently 
strong. Among these forces are the following : 

1. The useful load caused by the power transmitted from 
the point of receiving the energy to the point where the useful 
work is accomplished. 

2. Resistance due to friction in the machine. 

3. Forces due to inertia caused by change of velocity of the 
moving parts. 

4. Weight of parts of machines. 

5. Centrifugal forces caused by changes in direction of 
motion. 

The total action caused by the above forces is called the 
straining action on whatever part is considered. This straining 
action varies with the changes of working load, with the variation 
of position of the parts, with the change in speed, etc. In design¬ 
ing the various parts it is necessary to consider under what con¬ 
ditions the straining actions are greatest and calculate the dimen¬ 
sions of those parts to safely stand that action. 

It is obvious that the maximum working load must be less 
than the breaking load. In most cases it should be very much 
less. Generally it is much easier to determine (by means of test¬ 
ing machines) the breaking strength than it is the working stress. 
In order to be sure of sufficient strength, it is customary to divide 
the breaking strength by the factor of safety, to find the allowable 



16 


MACHINE DESIGN. 


working load. Results from actual cases provide us witli average 
factors of safety for various conditions. In case the straining 
actions are well known and the stresses are steady, the factors are 
small. A large factor is necessary when the straining actions are 
likely to be greatly in excess of the calculations, when the material 
is not reliable and when the parts are liable to shock. Some 
designers never use the term factor of safety, but know from 
experience that the various materials will safely carry a certain 
load under given conditions. 

In most cases a permanent set would be injurious; it might 
prevent the movements of some parts of a machine. Under these 
conditions it is evident that the working stress must be less than 
the elastic limit. 

riACHINE DRAWINGS. 

Machines are designed from principles obtained by successful 
practice and from mathematical calculations. In order that both 
the designer and the mechanic may have a clear idea of the work, 
the designer makes a drawing of the machine. The drawing 
indicates the size and shape of the various parts and how they are 
to be put together. By means of the drawing, the designer calcu¬ 
lates the relative motions of the parts and arranges them so that 
they will not interfere with each other. He calculates the sizes 
for strength and considers the modifications which will produce 
the greatest efficiency, or least cost of manufacture. The drawing 
indicates how the work is to be performed and distributed in the 
different shops. All dimensions, names of materials and finish 
marks should be clearly shown so that the workman, by carrying 
out accurately the ideas of the designer, may produce the desired 
machine. 

Usually several views of the part to be made are shown. 
Sometimes it is necessary to show sections in order that the inter¬ 
nal construction or sectional shape may be easily understood. 
These sections are usually drawn through the axis, or center, but 
it is sometimes advisable to show sections of other portions. 
Where the drawing shows a section, the portions of metal or wood 
supposed to be cut are covered with parallel lines at equal dis¬ 
tances and usually oblique. These sections are called hatched 
cross hatched, or simply sectioned. The character of the li nes 



MACHINE DESIGN. 


IT 


full lines? dotted, broken, light or heavy, indicate the material sup¬ 
posed to be cut. One kind indicates cast iron, another steel, 
another brass, etc. There is no standard for cross hatching, differ¬ 
ent draughtsmen using lines of various character. There is likely 
to be a confusion unless the parts have the name of the material 
printed on or near it, or a key is provided. 

Fig. 4 shows the lines as generally used; those representing 





STEEL 


BRASS 




COPPER 


LEAD OR 
BABBITT 



WOOD 


CAST IRON 
COMBINED 


Fh 


4 . 


cast iron, brass, wood and lead being almost universal, the others 
are subject to more change. The lines may run from left to right, 
or right to left; in case two or more parts of the same metal are- 
brought together it is necessary to avoid confusion by varying the 
direction and angles of the lines. If the hatching were to be the 
same, the parting line would be confused and one might think it 
all one piece. 

When drawing designs of the details, it is well to make them 
as large as is convenient. The scales in general use are full size; 
half size, 3 inches or 1J inches = 1 foot. A drawing is never 
made 1 size or by such scales as 2 inches or 1 inch = 1 foot. 

A working drawing is one that shows all the dimensions of 
an object in such manner that the object may be made by refer¬ 
ence to the drawing. It is a practical application of the study of 
projections. Usually three views are sufficient, elevation, plan or 
horizontal projection and end view. Besides these views, sections 
to show the interior construction are added. 



























18 


MACHINE DESIGN. 


It is not sufficient to draw the various views and sections the 
correct size; the dimensions also should be placed on the draw¬ 
ing. The workman can tell immediately the size of any given 
part without scaling it from the drawing. Although desirable, it 
is not necessary that a drawing be made accurately, provided all 
the dimensions are put in correctly. The chances of error are 
greatly reduced by removing the necessity to scale off dimensions. 

Dimensions should be used systematically and wherever nec¬ 
essary. In placing dimensions on drawings, a line should be 
drawn from one point to the other. The number representing the 
dimension is placed in the space left for it at the centre of the 
line. These lines should be either fine full lines or dashes about 
^ inch long. Arrow heads are placed on the ends of the line, 
the heads or vertex of the arrow just touching the points or 
lines. In case the dimensions are very small, the arrow heads may 
be outside instead of between the lines, or pointing toward each 
other. The dimensions should be written in feet, inches, halves, 
quarters, eighths, sixteenths, etc. of inches. Fractions should be 
reduced to lowest terms. Write |, not T 6 g, nor r fhe dividing 
line of the fraction should be parallel to the direction of the 
dimension line ; never an oblique line because the oblique line 
may be mistaken for some part of a number. Feet are repre¬ 
sented by the symbol inches by The inch marks should be 
placed after the fraction not between the whole number and the 
fraction; thus, eight feet, seven and three quarters inches should 
be written 8' — 7f", not 8' 7"|. When the length is even feet it 
is usual to write it 8' — 0" in order that the workman may know 
that the inches were not left off by mistake. 

It is necessary to get in all the important dimensions, espe¬ 
cially the “ over-all ” dimensions, so that the workman will not be 
compelled to add up several small dimensions in order to select 
his stock. 

Dimensions are often placed between two views and usually 
outside the several views. When placed outside, extension lines 
are used, that is, a fine or dash line is drawn as a continuation of 
lines or edges. 

In placing the dimensions of a circle, give the diameter, not 
the radius. When an arc is used, give the radius. Holes mav be 




MACHINE DESIGN. 


19 


located by giving the dimensions from the outside, or from the 
center of figure, to the center of the hole. The distance from 
center to center shows their distance apart. In case the holes are 
arranged in a circle, as in a cylinder head for instance, give the 
diameter of the circle whose circumference passes through the 
center of the holes. 

In making sectional views the plane of the section passes 
through the center line of a shaft, bolt, screw, or cylinder, and 
the cylinder part is not represented in section but in full. 

Sometimes, in addition to the above views an isometric or 
oblique projection is made. In the isometric projection only one 
view is used. The object is placed in such a position that its lines 
or edges are parallel to three rectangular axes. The dimensions 
are measured accurately on these lines, or lines parallel to them, 
and the lengths are true, not foreshortened, as in perspective 
drawing. Lines which represent length and breadth make angles 
of 30° with the horizontal and those representing thickness are 
vertical lines. 

Oblique projections are similar to isometric projections except 
that the lines which make angles of 30° with the horizontal in the 
isometric projection make angles of 45° in the oblique. 

It is usual when making mechanical or working drawings to 
do the work in pencil first, and then ink in the necessary lines, or 
a piece of tracing cloth is placed over the pencil drawing and the 
lines which show through are then inked. The latter method is 
used in case a number of blue prints are desired for the shops or 
office. 

In the pencil work, accuracy is necessary. Some beginners 
think they can correct inaccuracies in pencil by care in inking. 
The lines should be located exactly of the required length. A 
hard pencil; 4 H or 6 H is generally used. A hard pencil, when 
sharp, makes a depression in the paper which cannot be erased. 
For this reason press lightly on the pencil. 

In inking, it is better to make circles, arcs of circles and 
curved lines first . It is much easier to make straight lines meet 
arcs, or to make them tangent to circles or arcs, than the reverse. 
To indicate an edge or intersection of two planes a full line 
_is used; edges of intersections which are concealed are 




20 


MACHINE DESIGN. 


represented by dotted lines. Dot and dash lines* 

_. _ ._._. or_. .'_. ._ . ._. . indicate center lines 

or axes. A fine line or a series of long dashes- 

-is used for dimension lines. Titles, various views, sections, 

names of materials, etc., are lettered on the drawings. The styles 
and the care taken in this work varies with the draughtsman or 
with the amount of time at his disposal. In every case all let¬ 
tering should be neatly done and of some clear cut simple form. 
Marks indicating in which shop the work is to be done and for 
classification are also placed on drawings. Fig. 5 shows a work¬ 
ing drawing of a three inch pillow block which illustrates the 
above principles. The three views side, plan and end are half in 
section. 


DESIGN. 

Parts of machines are designed from rules derived from 
“ Strength of Materials,” other rules are based on the wear of the 
parts, while others depend on the size or thickness necessary for 
stiffness or a sound casting. In case theory doesn’t accord with 
the practice of successful designers, it is safe to follow the latter. 

Some parts of machines, bolts, nuts, screws, pipes, etc., can 
be obtained in standard sizes from various factories. The designer 
should know these standard sizes and make his details of such 
shapes that they will conform. The designer must also keep in 
mind the processes and tools to be used so that the construction 
will not be too difficult or expensive. 

Usually dimensions are expressed in feet and inches and such 
fractions of inches as i, |, Ag, A^. i, i, i or Ag are never used 
since the scales in shops are not divided in these fractions. 
Decimals are used only for great accuracy or in the design of gear 
teeth. 

All machines are made up of different combinations of simple 
principles. The designer must know these principles and the rela¬ 
tions they bear to one another. He must also have a thorough 
knowledge of the machine ; the work it is to do; the character of 
power to be applied and in some cases the location and surround¬ 
ings. A study of machines that have been designed to do similar 
work will be of great assistance. A wide knowledge of machines 












MACHINE DESIGN. 


21 










































































































22 


MACHINE DESIGN. 


permits the designer to have many ideas of details for the new 
machine. 

Often several complete drawings are necessary before the final 
result is attained. An idea that seems desirable may not prove so 
when the details are worked out. Sometimes the relative motions 
are all right, but when the parts are designed for strength, they 
are found to interfere with each other. The expense of construc¬ 
tion or the difficulties of manufacture may render a good design 
impracticable. 

All notes, calculations and sketches of details and combina¬ 
tions should be carefully preserved for reference. Ideas worthless 
for some particular machine may be found very valuable for an¬ 
other. It is well to keep sketches, calculations and memoranda in 
books rather than on loose sheets of paper that may become lost 
or misplaced. 

The estimates for weights and cost of machinery are made 
from drawings. The volume is found by mensuration and when 
multiplied by the weight of a cubic unit of the material gives the 
weight. Considerable skill and experience is sometimes necessary 
to estimate the volumes of irregular shaped parts. If the weights 
are known the cost is estimated from market values. The time 
necessary for completion is also judged from the amount of work 
and the ease with which it can be accomplished. 

At the beginning an inexperienced designer is usually taught 
by making drawings of details which have been designed by others. 
Often he is employed for some time simp’y tracing drawings. 
After a little he is given the principal dimensions of the simpler 
parts and instructed to make working drawings for the pattern, 
forge or machine shops. During this time he becomes familiar 
with methods adopted in shops, standard dimensions, allowable 
stresses for the various materials, methods of adjusting wear and 
lubrication, necessary dimensions for sound castings, etc. 

The following are a few practical rules or suggestions that are 
unconsciously kept in mind by the successful engineer, but are 
often forgotten by the inexperienced. 

Means for adjusting all parts subject to wear, should be pro¬ 
vided. 





MACHINE DESIGN. 


23 


Make the motion of all parts positive if possible ; avoid the 
use of springs and weights for producing motion. 

Provide means for lubrication wherever necessary. 

Construct the parts that may wear or break so that they will 
be accessible for adjustment or repairs. 

Cranks, belts, levers and gear wheels are preferable to cams, 
screws and worm-wheels. 

Avoid the use of tap bolts and studs ; use through bolts or T 
head bolts if possible. 

If convenient make the pressure per square inch on slides 
small. 

FASTENINGS. 

Bolts, Nuts, Keys, Cotters, etc. 

A screw is a cylindrical bar, upon the surface of which a Heli¬ 
cal projection called the thread has been formed. A cylindrical 
helix is the curve generated by the revolution of a point about the 
surface of a cylinder, while moving along the axis at a constant rate. 

A nut is a short hollow prism, upon the inside of which are 
formed grooves which corre¬ 
spond accurately to the 
threads of the screw. 

The screw and nut when 
used for fastening is called a 
bolt. Screws are also used to 
transmit motion and to adjust 
the relative positions of two 
pieces. Screw threads are 
usually triangular or square 
in section. The Whitworth 
and U. S. standard threads 
are triangular. Square 
threads are used chiefly to 
transmit motion. There is 
less friction and less wear 
than with triangular threads, 
but they are more expensive. 

The Standard Thread, Fig. 6, shows the American or Sellars 
triangular thread. The construction is shown enlarged by Fig. 7. 














24 


MACHINE DESIGN. 


The sides of the thread are inclined at an angle of 60°. The sec¬ 
tion of the thread is an equilateral triangle having its top cut off 
so that the flat portion is £ of the pitch in width. The angles at 
the bottom are filled in similarly. The real depth of the thread 
is a little less than the altitude p of the triangle ; it is .65 p. 

Sharp Y threads are those cut without the flat top and bottom; 
the section being an equilateral triangle. 

The pitch of a screw is the distance the screw advances dur¬ 
ing one revolution; it is the distance from one thread to the next. 
Another method of indicating the pitch is to give the number of 
threads per inch. For instance we say a screw has 11 threads 
per inch; that is, it will advance one inch during 11 revolutions 
or the pitch is -A- of an inch, or .091 inch. 

The pitch of threads depends upon the diameter of the bolt. 
The following equations give approximately the pitch, and the 
diameter at the bottom of thread in the U. S. standard. 


p = .^4 \! d .625 — .175 inch, 
d 1 = d — 1.3 p — d — 2 p x 

In these formulas p — pitch, d = diameter of bolt, d x = 
diameter at the bottom of the thread, and p 1 = real depth of the 
thread. 

Let n — the number of threads per inch ; then 

n = JL and d, — d —- UL 
P n 

The external diameter of a bolt is 1| inches, to find the pitch, 
the number of threads per inch, the diameter at root of threads 
and the depth of thread we proceed as follows : 

p = .24 y/l.875 -J- .625 — .175 = .204 inch. 

U = 5 (about) which makes the pitch .20. 


d 1 — d — 2 p x 
2\ Pl = d — dj 


Then the pitch is £ or .2 inch: there are 5 threads per 
inch, diameter at root of threads is 1.615 inches and the depth of 
thread equals .13 inch. 






MACHINE DESIGN. 


25 


The following table gives the principal dimensions of U. S. 
standard or Sellars threads. 


Diameter 

of 

Bolt 

(Inches; 

Number 

of 

Threads 
(Per Inch.) 

Diameter 
at Bottom 
of Thread. 
(Inches.) 

Area at 
Bottom of 
Thread 

(Square Inches.) 

1 

20 

.185 

.0269 

A 

18 

.240 

.0452 

3 

•g 

16 

.294 

.0679 

A 

14 

.345 

.0935 

h 

13 

.400 

.1257 

A 

12 

.454 

.1619 

I 

11 

.507 

.201? 

i 

10 

.620 

.3019 

i 

9 

.731 

.4197 

l 

8 

.838 

.5515 

n 

7 

.939 

.6925 

H 

7 

1.064 

.8892 

it 

6 

1.158 

1.0532 

H 

6 

1.283 

1.2928 

if 

5* 

1.389 

1.5153 

if 

5 

1.490 

1.7437 

H 

5 

1.615 

2.0485 

2 

H 

1.711 

2.2993 

2J 

4£ 

1.961 

3.0203 


4 

2.175 

3.7154 

2| 

4 

2.425 

4.6186 

3 


2.629 

5.4284 

8* 

3i 

2.879 

6.5099 

8j- 

8J 

3.100 

7.5477 

3| 

3 

3.317 

8.6414 

4 

3 

3.567 

9.9930 

4j 

n 

3.798 

11.3292 

4i 

2i 

4.027 

12.7366 

4 i 

2* 

4.255 

14.2197 

5 

2* 

4.480 

15.7633 

5j 


4.730 

17.5717 

5* 

2f 

4.953 

19.2676 

5} 

2f 

5.203 

21.2617 

6 

2J 

5.423 

23.0978 


The Whitworth triangular thread shown at D, Fig. 10, is 
used in England. The angle between the surfaces is 55°, and J 
of the depth or altitude of the triangle is rounded off instead of 























26 


MACHINE DESIGN. 


being flat as in the Sellars thread. The pitch and diameter at 
the bottom of the thread is found as follows: 

p = Md + .04, 

d, = d — = .M — .05. 

n 

A screw with a square thread is shown in Fig. 8 and an 
enlarged section of the thread in Fig. 9. The pitch of the square 
thread is usually double that of the triangular or V thread for a 
bolt or screw of the same diameter. The pitch is about £ the 


Fig. 8. 


Fig. 9. 




diameter of the screw; the diameter at the bottom of the thread is 
| the diameter of the screw and the depth of thread \ the pitch or 
-jo tlie diameter of the bolt. The edges of the square thread are 
slightly rounded to prevent flattening and to prevent binding of 
the nut. 

If the thread is to be subjected to very rough usage the 
rounding is carried further so that the section of the thread is like 






















MACHINE DESIGN. 


27 


that shown at A, Fig. 10. The thread shown at B is like a square 
thread, but instead of having a square section the thread tapers 
from the root to the point. This taper is given to the thread 
because it is easier to cut than a square thread. This form is 
often used as lead screws for lathes. The taper allows the nut, 
which is in two parts, to engage and disengage easily. The 



A B C D 


Fig. 10. 

trapezoidal or buttress thread is shown at C. It is used for 
transmitting motion or when the force acts always in the same 
direction. One face is normal to the axis of the screw and the 
other is inclined at an angle of 45 degrees. The top is usually 
cut off and the bottom filled in as in the U. 8. standard thread; 
the amount being about the same, that is, about 4- the depth. The 
pitch is equal to the theoretical depth since the angle of the face 
is 45 degrees. The real depth is about f the altitude of the 
triangle. 

The relative advantages of the various forms of threads; and 
the uses to which they should be put may be understood by con¬ 
sidering the forces which act on the faces. 

It has been proved that the greater the angle of the screw 














28 


MACHINE DESIGN. 


thread the greater the friction between the bolt and nut, and the 
greater the force tending to burst the latter. 

The friction of the square thread is less than that of the tri¬ 
angular thread because the angle between the sides is zero; there 
is moreover, no force tending to burst the nut. The triangular 
thread is, however, nearly twice as strong as the square thread. 
For the above reasons the square thread is better for transmitting 
motion and the triangular for fastening. 

The trapezoidal thread should be used only when the pressure 
comes on the side perpendicular to the axis. In this case the thread 
has the same friction as the square thread and the same strength as 
the V thread. If the pressure is put on the inclined side the friction 
and bursting force are greater than is the case with the Sellars 
thread having angles of 60° between the sides. 

Threads are formed for both right handed and left handed 
motion. Usually they are right handed. To determine the motion, 
hold the bolt or screw horizontal and turn it in the direction in 
which the hands of a watch revolve. If it advances into the nut 
or wood it is right handed. If when vertical the slope of the 
thread is from right to left it is right handed. For nuts reverse 
the above rule. 

riultiple Threads. In tracing the thread about the screw, 
the next thread is reached in one revolution, if the screw is single 
threaded. In other words, the nut will advance a distance equal 
to the pitch for every revolution of the screw. If in tracing the 
thread through a turn one thread is missed, it is a double threaded 
screw ; if two are missed it is a triple threaded screw, and so on. 

Multiple threaded screws are used for transmitting motion, 
when it is desirable to have the nut advance a considerable dis¬ 
tance for each revolution. This could also be accomplished by 
making the pitch large; but the multiple thread is better. The 
diameter at the root of the multiple thread is greater than that of 
a single thread and therefore stronger. The pitch is the distance 
the screw advances during one revolution, or it is the distance 
between two consecutive threads, if double threaded; or the dis¬ 
tance between three threads, if triple. 

Gas Pipe Threads. The Sellars thread is not suitable for 
the threads on gas pipe, for the calculated depth of thread would 



MACHINE DESIGN. 


29 


be greater than the thickness of the pipe 
system has been adopted having smaller 
pitch and cutting less deeply into the 
metal. 

Proportions of Bolts and Nuts. 

The diameter of the bolt determines the 
dimensions of the nut. These dimen¬ 
sions may va!ry to suit circumstances. 
Sometimes in cramped places the nut 
must be made thin, or there must be 
little metal around the screw threads, or 
it must be made of peculiar shape. In 
altering the shape or size of a nut, the 
designer considers the strain put on it, 
The standard form is shown in Fig. 11. 
The head of the bolt is square. Some¬ 
times the neck (the portion next the 
head) is made square also, to prevent 
rotation of the bolt when the nut is 
being screwed up. 

The nut is hexagonal and the 
washer circular. The washer is used 
with rough castings to give a smooth 
surface on which to turn the nut. The 
following are the formulas for dimen¬ 
sions corresponding to the figure, d being 
the diameter of the bolt. 


For this work a special 



For Rough Work. 


D = l\d + 1 " 

Dj — 1.73c? -f .14 " for hex¬ 
agonal 

D 1 = 2.12 d -f- .18" for square 


d„ - n d , 


h = d 


t = .15 d 


For Finished Work. 

D =l|d + J f " 

Dj = 1.73 d -f .07 " for hex- 
agonal 

T> 1 = 2.12 d + .09 " for sq. 

1>2 = U D, 

* = *-*.' 
t = .15 d 





























30 


MACHINE DESIGN. 


STRENGTH OF SCREW BOLTS. 


Bolts are generally used when the straining force is in the 
direction of the axis of the bolt; that is, bolts are used for tension 
stresses. It is evident that the effective area is not the area of the 
cross-section of the bolt, but the area at the root of the thread. 

Let P = the total load on the bolt. 
d 1 = diameter at root of thread. 
a — area of cross-section at root of thread. 

S w = safe working stress in pounds per square inch. 

Then for tension 

P = a S w = 7r _ ^1 S w f I’oni which a = JL. 

4 S w 


Then d 1 = 2 


The values of a are found directly from the preceding table. 

The value of P we can usually calculate from the machine. 
S w varies with the material and the conditions of stress ; if it is 
constant a good wrought iron bolt will stand 7,000 or 8,000 pounds 
per square inch. For variable stresses, S w may be taken as about 
5,000 or 6,000 pounds. Usually S w is taken as 4,000 or 5,000 
pounds. For bolts used in cylinder heads, S w varies from 3,000 
pounds per square inch for small to 6,000 pounds for large 
cylinders. 

Suppose we wish to find the diameter of a bolt to sustain a 
steady stress of 15,000 pounds, allowing 8,000 pounds as the work¬ 
ing stress. 


P _ 15,000 
S w 8,000 


1.875 square inches. 


The number 1.875 lies between 1.7437 and 2.0485 of the 
table. The larger value should be chosen, the diameter of the bolt 
being 1-J inches. 


EXAMPLES FOR PRACTICE. 

1. What is the safe working stress on a bolt 1 inch in 
diameter, if the value of P is 3,850 pounds ? 

Ans. 7.000 pounds (about). 







MACHINE DESIGN. 


31 





2. Find the size of bolt used for varying stress. P = 14,000 

pounds and S w = 4,000 pounds. Ans. 2| inch holt. 

3. An engine cylinder head is bolted to the 
cylinder by 12 bolts. If the total steam pressure 
is 48,000 pounds, what is the diameter of the bolts ? 

S w being 4,250 pounds. Ans. 1| inches. 

It would take considerable time to make the 
threads of all the screws and bolts of working- 
drawings accurately. To save time a conventional 
form, shown in Fig. 12, has been adopted. The 
threads are represented by alternately light and 
heavy lines. The distance between these lines 
need not be equal to the pitch of the threads, 
because, the diameter being given, the number 
of threads per inch is found from the table. If 
the threads are not standard the number of threads 
per inch is noted on the drawing. 

WRENCHES. 

Forms of solid wrenches or spanners are 
shown in Fig. 13. The dimensions are given in 
decimals of the diameter of the bolt. They 



Fisc. 12. 




are made in many sizes, with ends shaped for hexagonal and 
square nuts. The unit for the proportions is D. 

FORMS OF NUTS. 

The most common form of nut is the hexagonal shown at A, 
Fig. 14 ; B shows the square nut. Usually both square and 


























32 


MACHINE DESIGN. 


hexagonal nuts are chamfered off at an angle of 30 to 45.° Some¬ 
times they are finished with a spherical bevel, having a radius of 
about twice the diameter of the bolt. C shows a round nut hav¬ 
ing holes in the sides into which a bar is inserted for tightening 



Fig. 14. 


the nut. The nut shown at D is called a cap nut; it is used to 
prevent leakage past the screw thread. A thin copper washer is 
sometimes used with this form of nut. E represents a flange nut 
which is used when the hole in which the bolt is placed is consider¬ 
ably larger than the bolt. The flange covers the hole and gives 
greater bearing surface. 

FORMS OF BOLT HEADS. 

Fig. 15 shows several forms of bolt heads. The hemispheri¬ 
cal or cup-shaped head, a common form, is shown at A. At B is 



Fig. 15. 


shown the hexagonal form. It is similar to the hexagonal nut 
and has about the same dimensions except the height which is 
usually less; it is from f d to d. The cylindrical bolt head is 




























































































MACHINE DESIGN. 


33 


shown at C; rotation of the holt is prevented by the square neck. 
D shows the spherical head; the bearing surface rests on a seat of 
the same shape. It is used when the bolt tends to lean toward 
one side. The head remains in contact with the seat for every 
position of the bolt. E shows a bolt with countersunk head; 
rotation is often prevented by a set-screw. 

Fig. 16 is the hook bolt. It is used when a piece would be 



Fig. 16. 


Fig. 17. 


weakened or is too small to have a drilled hole. Fig. 17 is a 
T=headed bolt. 

Set=screws are screws or bolts used to prevent by friction 
relative rotation between pieces. Set-screws are often used to 
prevent the hub of a pulley from turning on the shaft. They 




are screwed through the hub and prevent rotation by pressing 
against the shaft. At A, Fig. 18, is shown the cone point set¬ 
screw. The one shown at B is called the cupped set-screw; C, 
the headless cone point set-screw; and D, the roimd point set- 
screw. 

A stud bolt is one that has threads cut on both ends. One 






























































34 


MACHINE DESIGN. 


end is screwed into one of the pieces to be connected and remains 
in position when the nut is 
on or off. Fig. 19 shows a 
stud bolt. They are some¬ 
times used for cylinder-heads 
and valve-chest covers. A 
stud with a collar is shown 
in Fig. 20. The collar may 
be square or round; if square 
it is a convenient place for a 
wrench. The collar forms a Flgt 19, Fig. 20. 

shoulder against which the stud may be screwed. 

Fig. 21 shows an ordinary method of 
fastening a bolt to stonework. The head, 
which is long, is made jagged with a cold chisel. 
The hole is made larger at the bottom than at 
the top and after the head is placed, the space 
around it is filled with melted lead or sulphur. 

Foundation bolts, which are used to fasten 
an engine-bed to its foundation, are often fixed 
as shown in Fig. 22. The head is formed by 
a cast iron washer and a cotter. This cotter 
passes through a slot and has gib ends to pre- 
Fio . 4>1 vent slipping. The washer jjrovides a large 

bearing surface. The bolt, washer, and cotter 
are placed in a recess in 
the wall and are acces¬ 
sible. The size of the 
washer is easily deter¬ 
mined. The area of the 
washer multiplied by the 
compressive or crushing 
strength of the stone or 
brick should be equal to 
the pull on the bolt. 

The tensile strength of 
wrought iron is about Fi g. 22 < 

55,000 pounds per square inch and the compressive strength of 























































MACHINE DESIGN. 


35 


brick is about 2,500 pounds per square inch, or about ^ of that 
of the bolt. Therefore, the bearing surface of the washer should 
be about 22 times the area of the cross-section of the bolt. 

Screws. The three most common forms of machine screws 



are shown in Figs. 23, 24, and 25. Fig. 23 is the countersunk 
head screw; Fig. 24, the fillister head and Fig. 25 the button 
head. The countersunk head is used when the head is not to 
project above the plate. 


LOCKING ARRANGEMENTS FOR NUTS. 


Nuts never fit the bolt accurately; some clearance is neces¬ 
sary to permit them to turn freely. If a nut is subject to frequent 
changes of load and vibration it gradually unscrews or slacks 
back. To prevent nuts from becoming loose various locking 
devices are used. 

One of the most common is the double nut called a locknut 




Fig. 28. 


or jam nut shown in Fig. 26. There are two nuts, one about 



























































86 


MACHINE DESIGN. 


twice as thick as the other. The outer nut should be the thicker 
because the load is thrown on it. However, the thin one is often 
placed on the outside because the wrench is often too thick to act 
on it when it is inside. When the nuts are screwed home they 
are locked together by being turned in opposite directions. 

In Fig. 27 the nut is kept in place by a split pin or cotter. 
A hole is drilled through the bolt and the pin driven through and 
the ends turned over to prevent it from backing out. This is not 
a very good method because the nut must always be close to the 
pin. 

Another method is shown in Fig. 28. The nut is sawed 
about half way through and the parts closed slightly by a set¬ 
screw, after the nut is screwed home. The nut then grips the 
thread tightly. For small nuts the set-screw is not used but the 
parts are closed, just before it is set, by a slight blow of a 
hammer. 


At A big. 29 is shown a Grover’s spring washer. The upper 



Fig. 29. 


portion of the figure shows the washer when not held down by the 
nut. When the nut is screwed down tightly, the washer becomes 
nearly flat and its elasticity increases the friction between the 
threads of the bolt and nut. 

In the device shown at B, Fig, 29, a stop plate is used. It 
is fixed by a set-screw to one of the pieces through which the bolt 
passes. It is shaped so that the nut may be locked at intervals of 



























MACHINE DESIGN. 


37 


iV °f a revolution. The set screw may have a diameter equal to 



d being the diameter of the bolt. The other dimensions are also in 
terms of the diameter. For bolts set in a circle, the bolts of a 
cylinder head for example, a circular stop plate, shown at C, Fig. 
29, is used. It is placed inside the nuts and bears against one of * 
the parallel sides. 

There are numerous methods of locking by set-screws, their 
forms depending on the position of the pieces. 

Usually bolts are used in tension, that is, when the strain¬ 
ing force is parallel to the axis of the bolt. The joint pin is a 



Fig. 30. 


bolt placed so as to be in shear. Fig. 30 shows a knuckle joint. 
The joint pin is made the same size as the rods because of wear. 
If the pin were subjected to simple shear at the two sections it 
need be only about .7 the diameter of the rod, but it soon wears 
and is subjected to bending stresses also. 

The other proportions are in terms of the diameter of the rods. 
d — diameter of the rods. 
a =1.2 d 
b = 1.1 d 
c = .75 d 
e — .S d 

i — .6 d 
o = 1.5 d 











































38 


MACHINE DESIGN. 


Keys are small wedges, usually made of iron or steel, used to 
fix wheels, cranks and pulleys to shafts. It is the duty of keys to 
prevent the wheel or crank from rotating otherwise than with the 
shaft on which it is keyed. For example, a crank is keyed to the 
shaft in order that the shaft and crank will rotate together. 

. Usually the friction of the key in the keyway will also prevent the 
wheel from sliding along the shaft. 

Keys are usually plain rectangular pieces with their lateral 
sides parallel and a tapering thickness. In case the small end is 



inaccessible, that is, the arrangement is such that it cannot be 
driven out, the key is made in the form shown in Fig. 31. A 
gib head is made at the large end which forms a shoulder to drive 
against. 

Fig. 32 shows several forms of keys. The concave, or saddle 
key, is shown at A. The slot or keyway is cut in the wheel and 
the key hollowed to fit the shaft which is not cut at all. As the 
key holds by friction, it is suitable only for light work. The flat 



Fig. 32. 


key is shown at B. A flat surface is planed on the shaft having 
a breadth equal to that of the key. This form is more secure than 
the saddle-key. The sunk key shown at C is more effective than 
either of the above forms because slipping is prevented unless the 
key shears. There are two forms of sunk keys, the rectangular 
and the square. The rectangular form is used for fastening 








MACHINE DESIGN. 


39 


cranks, gear wheels, pulleys, etc. They are driven in tightly and 
fit both at the top and bottom as well as the sides. As they fit 
on all sides they should not be used in accurate work because they 
are likely to spring the work out of true. Square keys are used 
for accurate work; they fit accurately only on the sides. In case 
a pulley is accidentally bored a little too large for the shaft it is 
fastened securely by using both a flat key and a sunk key as 
shown at D. The two keys are placed at about right angles. 
The pulley and the shaft have a bearing at three points on the 
circumference of the shaft. 

Sometimes large wheels are keyed to the shaft by two, three 
or four keys. When the shaft is square eight keys may be used. 



If they are arranged as shown in Fig. 33 no keyways need be cut 
on the shaft, and only the key seats are planed. 

Pin=keys. A round taper pin is used in place of a key for 
small shafts; handles on valve stems for instance. The pin is 
sunk half in the shaft and half in the piece, as shown in Fig. 34. 

Sometimes a secure connection, where the parts are not to be 
separated, is desired, as is the case with small cranks. The crank 
is bored slightly smaller than the crank shaft, then expanded by 
heat and shrunk on. It is further secured by a key or pin. 

In order that keys may be easily driven in and removed 
they are tapered slightly. The taper is about 1 in 64 to 1 in 150. 
The more accurate the work the less the taper. This method of 
expressing taper means that the decrease in thickness is -fa to 
of the length. Sometimes taper is expressed in inches to the foot 
as inch per foot. 

Sliding Keys. Sliding or feather keys are used if the piece 







40 


MACHINE DESIGN. 


is to be prevented from rotating but at the same time is to be 
allowed to slide along the shaft. The key may be fastened to the 
piece and free to slide in the keyway of the shaft, or it may be 
fast to the shaft and the wheel free to slide. Figs. 85 and 36 
show the various methods of fixing the key. In Fig. 36 the key 




is dove-tailed in section and is fastened to the hub. The one 
shown in Fig. 36 is used when the hub comes against a collar or 
bearing, since it does not project from the hub. The feather 
key of Fig. 35 has gib heads. 

Strength of Keys. Saddle keys are used most where the 
stress between the pieces is usually small. No exact rules can be 
given as they depend on friction to prevent rotation. 

Sunk keys must resist both shear and compression. The 
twisting of the shaft tends to shear the key and crush it. 

Let b = width of key in inches. 

I = length of key in inches. 
t = thickness of key in inches. 

S 8 = allowable shearing stress in pounds per square inch. 
S c = allowable crushing stress in pounds per square inch. 
d = diameter of the shaft in inches. 
r = radius of wheel or pulley in inches. 

F = force in pounds acting at the rim. 






























MACHINE DESIGN. 


41 


The resistance to shearing is the shearing area multiplied by 
the shearing stress, bl$ 8 . To find the diameter of the key, take 
moments about the center of the shaft and solve for hi 

2 d X blS 8 = F r, from which bl — ^ ^ —. 

d S s 

The sunk key usually has ^ the thickness in the shaft and | 
in the hub. In case the key is designed to be equally strong to 
resist shearing and crushing the shearing strength must be equal 
to the crushing strength. 

The resistance to shearing is blS 8 ; and the resistance to crush¬ 
ing is equal to the product of the bearing surface and the stress, 
or 1 tlS c . 

If the crushing stress is assumed to be twice the shearing 
stress, S c = 2S s , then b — t and the key is square in section. 
Usually the key is made wider than the thickness so that the 
shearing strength shall be greater than the resistance to compres¬ 
sion, as there is little danger of crushing. 

Let H. P. = the horse-power transmitted. 

N = the number of revolutions per minute. 
r — the radius of wheel in inches. 

Then as the circumference of a circle is 2 it r, a point on the 


circumference will move 2 ir r N inches or 


2 7r r N 
~T2“ 


feet 


per 


minute. 

The power transmitted (assumed to be constant) will be the 
force acting, F, multiplied by the distance = ^ or, 


F X 


N 


12 


= foot-pounds. 


One H. P. = 
Then H. P. = 


33,000 foot-pounds per minute. 

2,rrNF 33,000 = ^ 

12 198,000 


or, 


TrrNF = 
Fr = 


198,000 X H. P. 
198,000 H. P. 


H. P. 


F r = 63,025 











42 


MACHINE DESIGN. 


For shearing of keys the usual factor of safety is about 10 
which gives an allowable stress of about 5,000 pounds per square 
inch for wrought iron and about 7,000 pounds per square inch for 

2F r 

steel. Inserting these values in the equation bl = 


d S t 


bl 


Then bl 


Fr 


d X 2,500 
Fr 

d X 3,500 
25.2 H. P. 
d X N 


, for wrought iron 
, for steel. 

, for wrought iron 


18 H. P. , , , 

= __, tor steel. 

d X N 


Suppose the pressure on a crank-pin is 15,000 pounds and the 
crank is 12 inches long. If the shaft is 6 inches in diameter and 
the length of key 6 inches, what should be the dimensions of the 
wrought iron key ? 

2,500 d 


b 


Fr 

2,500 X l X d 


15,000 X 12 
2,500 X 6 X 6 


= 2 inches 


Then the key should be 2 inches broad. Its thickness is * 
usually some fraction of the breadth. We will make it -|, or 1-t 
inches. Keys vary in thickness from 1 to J of the breadth. 

In designing machinery, the dimensions are usually deter¬ 
mined by empirical formulas. For the ordinary sunk key b — 

\ d Yi ail d the mean thickness, t = P to | b. 

If we use these formulas for finding the dimensions of the key 
in the above example, 5=-|d + ^= -JX 6 + ■§• = If inches. 
t = f l = || = 1^ inches. 

When pulleys are keyed to large shafts which transmit only 
a small amount of power, the dimensions obtained from the above 
formulas are larger than necessary. In such cases the following 
formulas are used. 


-y 


100 H. P. 
N 


or, 




Fr 


360 


These values of d are inserted in the above formulas. 















MACHINE DESIGN. 


43 


A pulley transmits 3 horse-power. It is keyed to a shaft 6 
inches in diameter, which makes 130 revolutions per minute ; find 
the dimensions of the key. 

^ — \d-\~Y — = -455 or | inch (about). 

t = t b = i inch. 

EXAMPLES FOR PRACTICE. 

1. A shaft is 4 inches in diameter ; what is the breadth of 

the sunk key? Ans. 1^ inches. 

2. Find the breadth of a steel key, when the length of the 
key is 4 inches, the horse-power transmitted is 100, the shaft is 
4J inches in diameter and makes 100 revolutions. Ans. 1 inch. 

COTTERS. 

A cotter is an iron or steel bar driven through one or both 
of two pieces to be connected. It prevents their separation by its 
resistance to shearing at two transverse cross-sections. Cotters 
sometimes adjust the length of the pieces connected. They should 
be so designed as to decrease as little as possible the strength of 
the connected pieces. 



Fig. 37. 


A and B of Fig. 37 show two views of a simple cotter. In 
this form the cotter passes through the rod. The cotter resists 
tension. The collar or enlargement prevents movement in the 
















































44 


MACHINE DESIGN. 


other direction, and therefore resists thrust. An arrangement 
designed to resist tension only is shown at C, Fig. 37. The 
cotter has gib ends to prevent its moving out of place. 

A construction to resist tension alone is shown at D and E of 
Fig. 38. This cotter is divided; one part with hooked ends is called 



Fig. 38. 


the gib and the other a plain cotter. Such a construction is often 
called the gib and cotter. At F of the same figure, the rod is 
tapered to provide for thrust. 

Cotters like those shown at D and E in Fig. 38 are long 
and tapered and therefore may be used to adjust the length of the 
connected pieces. By driving the cotter in, the total length of 
the pieces is made less. 

A cotter is often used to connect two straps, a and b , to the 
rod Z, as shown in Fig. 39. 

If a plain cotter is used the 
excessive friction between 
the cotter and the straps, 
when the former is driven 
down, causes the lower strap 
to open as shown by the 
dotted lines. To prevent this 
a gib and cotter are used, or 
two gibs and a cotter. The 
gib prevents the strap from 
spreading. In Fig. 40 the 
side, a b, of the gib and the side, c d , of the cotter are parallel to 
each other and are at right angles to the straps. The parts of 
the gib and cotter that are in contact are tapered. 




















































MACHINE DESIGN. 


45 


Taper of Cotters. A cotter that has a taper of more than 1 
in 7 is likely to slack back. In general, the taper is from 1 in 24 
to 1 in 48. If the cotter has a fastening device it may have a 
much greater taper, i. e., 1 in 6 or 1 in 8. The taper of the cotter is 
found by dividing the increase in width by the length. Thus if 
a cotter is 2| inches in width at one end and 2| at the other the 
increase is i inch and if the cotter is 10 inches long the taper is J 
divided by 10 = Aq or 1 i n 20. 

Strength and Proportions of Cotters. In designing cotters a 
few facts must be remembered. 


In the following demonstration the letters refer to Fig. 42. 

The cross-section, b t, must be sufficient to stand the shear¬ 
ing stress. 

The thickness, £, must be large enough to prevent crushing. 

The diameters should be so designed that the rod will not be 
weakened by the cutting of the slot for the cotter. 

Let F the force in pounds on the rod, 

S t = allowable tensile stress of the rod in pounds per square 

inch, 

S c — allowable compressive stress of the cotter or rod in 
pounds per square inch, 

S s — allowable shearing stress of the cotter in pounds per 
square inch, 

The net area of the rod is the area of a cross-section minus 
the area of the slot or, 


net area = 


7T d 2 


dt . 


The shearing area of the cotter is 2 b t. The area subject to 
crushing is d t. The area of the socket subject to tension is 


2L (D 2 — d 2 ) — (D — d) t. 

7T<V 

4 


The area of the rod itself is 


Then, as each of these values when multiplied by its 





46 


MACHINE DESIGN. 


respective allowable stress must be equal to the force, F, 



!'f -■"! 


(a) 

F = 2i(S s , 


O) 

F = i « S c , 


00 

F= j 

j £<?>*-<**) 

— (D — d) t 

J St, (d) 

F = |-<V S t , 


00 

If the cotter is subjected to a 
allowable stresses may be, 

force in one direction only, the 

Wrought Iron 

S t = 10,000 

S s = 8,000 

S c = 20,000 

Cast Iron 

S t = 2,800 


S c = 5,600 

Steel 

S t = 18,200 

S s = 10,600 

S c = 26,400 


In case the forces act alternately in opposite directions the 
stresses are found by dividing the above values by 2. 


The above values show that, 


S, 

St 


i and = 2, 


then 


S 

— 5 — 01 

s: “ * r- 


Then combining equations (b) and (c) and letting t = | d 
we have, 

• 2btS 8 =:dtS c 
or b = J|s = I d = 1.25 d, 

A O e 


Combining (a) and (c) 
7 r d 2 


d t = d t _5 

St 

t = ^ — \d (about). 


Combining (a) and (d) and taking t — 


7r d 


j 7T d/ 2 

(“T 


it d' 2 

~w 


8* = 


j-J- (D»—i*)_(D —d) 



D — | d. 







MACHINE DESIGN. 


47 


To have the same tensile strength D should equal ^ d but to 
prevent crushing, the bearing surface of the socket must equal 
that of the rod, or 

(D — d) t — d t, 
and D 2 d 


Combining (a) and (e) and, as before, taking t = 



( 7 r d 2 7 r c? 2 ) c 7r d 1 2 Q 

| — St ’ 

d t — .816 d. 

Since the bearing surface of the collar should be equal to that 
of the cotter in the rod, 

JL. (d 2 2 — d 2 ') = d t, and since 

_ 7 t d 

12 ~’ 

d 2 — 1.15 d. 



b = l\d 
t = \d 
D — 2 d 


d x = .816 d 
d 2 = 1.15 d 

a is made equal to c and is from f to l£ d. 









































48 


MACHINE DESIGN. 


Fig. 41 shows a cotter with double gib. In this case b t is 
usually made the sectional area of the strap and t = I b. b is 
made the same for all cases, whether a single cotter, gib and 
cotter or two gibs are used. The other dimensions are, 



b 

6 T 

* - 1 5 6 5 

0 = t 5 <t 5 

l — f l 

If a steel cotter is used in a wrought iron rod, b may equal d. 




Fig. 48 shows a small split pin. Split pins are forms of 
cotters which are used to prevent two pieces from separating but 









































































MACHINE DESIGN. 


49 


tlo not connect them firmly. Large pins are made solid with a 
slight taper. 

Locking Arrangements for Cotters. Fig. 44 shows a method 



Fig. 44. Fig. 45. 

of securing the cotter by a set screw. The cotter passes through 
the head of the gib and is held by the screw. A simple way to 
secure the cotter is by prolonging the gib and having a screw 



thread cut on it as shown in Fig. 45. Nuts on each side of the 
bent cotter keep it in place and adjust the length. In Fig. 46, 
the end of the cotter is a screw which passes through a recessed 
washer or extra seat. A nut above the washer holds it in place. 
In case a cotter has an excessive taper this method is sometimes 
used to prevent slacking back. 











































50 


MACHINE DESIGN. 


EXAriPLES FOR PRACTICE. 

1. Find the dimensions of a rod and cotter of the form 
shown in Fig. 42. Assume S t = 6,500 pounds. The load is 
7,900 pounds. 

' d = 1J inches 

d^ — 1| inches 

d 2 = 1J inches 

Ans. D = 3 inches 

t — | inch 

b = lj inches 

a — li to If inches 

2. Two straps are connected to a rod as shown in Fig. 41. 
If the pull on the rod is 10,000 and S s = 5,500 pounds, find the 
dimensions of the cotter and gibs. Assume t — i inch. 

(t — ^inch. 

. j width of cotter — if inches. 

ns | breadth of gibs = li inches. 

\^b = 3f inches. 

3. What are the dimensions of a wrought iron cotter used 
to fasten a wrought iron rod 2 inches in diameter ? 

a \ t = i inch 
ns * | b = 21 inches 

4. A cotter is 1|- inches wide at the middle; it tapers on 
each side. If it is 18 inches long and tapers inch to the foot 
what is its width at each end ? 

Ans. 1^ inches and 1^ inches. 

JOURNALS. 

Journals are the portions of shafts and axles which turn in 
bearings and are supported by the frame of the machine. They 
are usually cylindrical but may be conical or spherical in form. 

If the journal is at or near the end of the shaft it is called an 
end journal; if situated between two end journals it is called a 
neck journal. 

The most common form for the bearing portion of a journal 
is a true cylinder as shown in Fig. 47. Collars or shoulders at 
the ends bear against the ends of the brasses, in which the journal 
revolves, and limit the play lengthwise. In case a light end play 





MACHINE DESIGN. 


51 


is desired, as in the car journal for instance, the bearing is made 
slightly shorter than the journal, thus permitting a little longitudinal 



Fig. 47. 


motion and causing uniform wear of the brasses. When longi¬ 
tudinal motion would interfere with the movements of other por¬ 
tions of the machine, it is made as small as possible. 

The methods for calculating the requisite size of a journal 
depend upon the velocity of the shaft and the constancy with 
which it is run. In case it runs occasionally or at slow speed it 
is designed for strength; but if it runs constantly at high speed, 
durability and freedom from heating are as important elements as 
strength. 

Journals may be subjected to straining forces in the plane of 
the axis (causing bending and shearing stresses) and also to com¬ 
bined torsional and bending stresses. 

When designing for strength the journal is considered as a 
cantilever beam uniformly loaded. 

If l == the length of the journal in inches, 
d = the diameter of journal in inches, 

S = the safe working stress, 

I = the moment of inertia, 

c = the distance of the fibre most remote from the neutral 

axis, 

W = the total load in pounds, 
w = load per square inch in pounds ; 
then from “ Mechanics,” 

C T 

W = 2 * x —, 

l c 


and since for a circular section, 

7T C? 4 


I = 


and c = 


64 















52 


MACHINE DESIGN. 


then, 


w _ 9 S v 2 TT d* _ 7T cT 3 S 

“ T “64 ~d 16T 


and, 16 W l — tt d s S 


from which d = 


v/ 


16 W 
7T S 



The equation is used in the above form because the ratio of 

length to diameter is usually assumed, i. e., fixed before the 
d 

calculation is made. If this ratio were not assumed there would 
be two unknown quantities in the equation. 

For journals which work intermittently the ratio l to d is 

usually 1, or — — 1. Where the speed is less than 150 revolu- 
d 

tions per minute — varies from 1.5 to 1.75. The greater the 
d 

speed the greater the proportion of length to diameter ; this causes 
a reduction of pressure per unit of bearing surface as the speed 
increases. 

For example. Find the length and diameter of a steel jour¬ 
nal, having a load of 2,000 pounds. Assume -i-to be 1.5 and the 

d 

safe working stress, S, as 9,000 pounds. 


d 




16 W 



v/ 


16 X 2,000 
3.1416 X 9,000 


X 


— = 1.3 inches. 

2 


In this case the journal would be ly 5 g inches in diameter and 
1 t6 X 1.5 == 2 inches long. 

The safe working stress varies with the conditions and the 
material. Average values of S are as follows: 


Material. 

Steel 

Wrought Iron 
Cast Iron 


Constant Load. 

12,000 to 13,000 
7,000 to 9,000 
3,500 to 4,500 


Variable Load. 

9,000 to 12,000 
6,000 to 7,000 
3,000 to 4,000 


When designing to provide against heating, experience deter¬ 
mines the allowable pressure per square inch on the area of pro- 










MACHINE DESIGN. 


53 


jection of the journal. This is called the projected area and is 
equal to the length of the journal multiplied by the diameter, or, 

area = l X d. 

The load per square inch evidently is the total load divided 
by this area, or, 

W 

w =_ 

l X d 

If the pressure per square inch w, is too large the lubricant 
is squeezed out and the journal is likely to heat and increase in 
size. The better the lubricant, the larger w may be. For high 
speeds the pressure may be greater than for low speeds. In the 
case of journals, as for example, crank pins, where the pressure 
alternates in direction the limit of pressure may be about twice as 
great as where the load is in a fixed direction. This is because of 
the better lubrication in case of alternating direction. 


Since W = w l d, and W = 


it d s S 
16 l 


~r AZ Q 

then wld= „ » or 7 t d 2 S = 16 w 


16 l 


, l 2 IT S l 

and — = - TS —, or 

d 2 16 tv d 


->! 


IT S 
16 w 


Substituting this value of — in the equation d — ■%/— 

d V 7 r 

the result is, d = 2y/ 


16W l 
S ~d 


w 

sf ir S w* 


and since w l d — W, 
W 


l = 


w d 


Therefore in calculating the diameter when the pressure w is 


assumed we use the formula d 


= 2 V /^UancU= * 
' \TT S W w a 


for 


the length. 

Find the length and diameter of a steel journal when the 













54 


MACHINE DESIGN. 


load is 11,000 pounds. The safe working stress is 10,000 pounds 
and the allowable pressure is 900 pounds. 

From the formula we obtain; 




_11,000_ 

v x l",ono x 


The square root of nr = 1.77245, then d — 2.87 -f- inches, 
and the shaft would be 8 inches in diameter. We also find 


l = 


W 

w d 


11,000 

900 X 3 


= 4.07 


— 4Ag inches long. 


The following table of limits of pressure per square inch of pro¬ 
jected area for different conditions is taken from Unwin’s Machine 
Design. 


PRESSURE ON BEARINGS AND SLIDES. 


Pressure Calculated in lbs. per sq. in. op Bearing Surface. 


Intensity 
of pres¬ 
sure, lbs. 
per sq. in. 


Bearings on which the load is intermittent and the speed 
slow, such as crank pins of shearing machines .... 

Cross-head neck journals. 

Crank pins of large slow engines. 

Crank pins of marine engines, usually. 

Main crank shaft bearings Marine engines (slow) .... 

Main crank shaft bearings Marine engines (fast) .... 

Bail way journals . . . 

i 

Fly wheel shaft journals. 

Small engine crank pins. 

Slipper slide blocks, Marine engines .. 

Stationary engine slide blocks. 

Stationary engine slide blocks, usually. 

Propeller thrust bearings. 

Shafts in cast-iron steps (Sellers).. 


3000 

1200 

800 to 900 
400 to 500 
600 
400 
300 

150 to 250 
150 to 200 
100 

25 to 125 
30 to 60 
50 to 70 
15 


































MACHINE DESIGN. 


55 


NECK JOURNALS. 

A neck journal is considered as a simple beam supported at 
both ends and uniformly loaded. The cross head pin, or wrist pin 
is an example of this kind of journal. 

From u Mechanics,” the equation for the above beam is, 

W = 8 JL X — 
l c 


Since I — , and c = 

64 2 

W = 8 T x TF- 


from which d 


=V- 

’ 7T 


W y l 
S x d 


This formula is used to calculate the value of d when the 

ratio — is assumed. 
d 

Example. Find the diameter and length of a wrought iron 
neck journal when the load is 4,400 pounds, S assumed to be 8,000 

pounds and = 2. 


Solution, d 




4,400 


X 2. 


3.1416 X 8,000 
= 2 X -59 = 1.18 inches. 

A l T 3 g inch shaft would probably be chosen. 

Then, also, l = 2 d, 2 X l T 3 e — 2| inches. 

As in end journals W = w d l , and since W = 8 ^ ^ ** 


32 l 


equating the two values for W, we get, 

, 8 S 7r d z 

w l d — 


32 1 ’ 

4 w l 2 = 7r d 2 S. 


™ l 2 7T S 
Then — = -— 
d 2 4 w 


and — 
d 




7r S 













56 


MACHINE DESIGN. 


Substituting this value of —— in the equation d — 2 y/ —— X — 


we get, d — 2 v/“^ X \/ 

* 7T S 


7T S 

4 w 


W 


and reducing, d = 2 v/ 

* > v/IttSw 


as before, / = 


W 

w df' 


The same values for S and w, given for end journals may be 
used for neck journals. 

Suppose we wish to find the length and diameter of a neck 
journal having a load of 8,000 pounds. Let us assume S to be 
8,500 pounds and the bearing pressure 500 pounds ; then, 


W 


8,000 


' V y/4 j S w V y/4 X 3.1416 X 8,500 X 500 
= 2 y/l.09 = 2.08 inches. 

A 2-| inch shaft would be used, and we also find 




8,000 


w d 500 X 2| 


__ — 7J inches (about.) 


DIHENSIONS OF JOURNALS. 

We have already seen how the diameter and length of jour¬ 
nals are determined. Knowing the diameter, the height of the 
collar may be found from the formula h = .1 d + -J" and the 
breadth equals 1| times the height. 

Usually the journal is turned with a fillet in the corner, since 
the shaft is less likely to crack than if it has a square corner. The 
radius of the circular fillet is about one half the height. 

FRICTION OF JOURNALS. 

In every case, friction generates heat which causes the 
temperature of the journal to rise. This rise of temperature 
increases the size of the journal and causes unnecessary work. 

In order to diminish friction, the journal is lubricated, that 
is, it is supplied with some lubricant (oil or fatty matter) which 
forms a thin film between the journal and the bearing. The 
lubricant diminishes friction and greatly reduces wear. 













MACHINE DESIGN. 


57 


The surface velocity in feet per minute of a journal is evi¬ 
dently the circumference of the circle whose diameter is d , multi¬ 
plied by the number of revolutions ?i, or expressed algebraically, 

Surface velocity := feet per minute. 

If f — the coefficient of friction, and W the load, the work 
expended in friction is expressed by the formula : 

7r dn 


Work = / W X 


12 


foot ponnds per minute. 


As we have seen from the table on page 54, the pressure 
per square inch on the bearing surface cannot exceed certain 
limits. These limits varying with the kind of work done and the 
speed. For the load W a certain bearing surface dl is necessary. 

The value of the coefficient/varies greatly; it is dependent 
upon speed, pressure, kind of metals, and kind of lubricant. 
Under some conditions it may be as low as .001 and under others .2. 

From the above equation it is evident that the work used in 
friction is directly proportional to the diameter of the shaft. This 
fact shows that under a constant load it is well to obtain a large 
projected area, d £, by increasing l and making d as small as is 
consistent with strength. 

Suppose we have two journals, 1| inches in diameter and 4| 
inches long; the other 3 inches in diameter and 2.25 inches long. 
They have the same projected area, i.e ., 6.75 square inches; but 
the work required to overcome friction of the first is only one-half 
as much as for the second. 

Although the first, i. e., the 1-| inch journal is preferable for 
a steady load, it is not as strong as the three inch journal, and the 
latter should be used for high speeds and when the journal is sub¬ 
ject to shocks. 

PIVOT AND COLLAR JOURNALS. 

In journals already considered the 
direction of pressure is perpendicular to 
the axis of the shaft; in the pivot journal 
shown in Fig. 48 the direction of pressure 
is parallel to the axis. With end journals 
the bearing surface is the cylindrical Fig. 48. 



























55 


MACHINE DESIGN. 


surface ; but in pivot journals it is circular, and is the area of the end 
of the pivot. To find the diameter of such a journal knowing the 
load, assume a value for the pressure per square inch of bearing 
surface and solve for the area. This may be expressed by the 
formula, 

w 7T d 2 - 

W = —_— X w 

Suppose the total load is 32,000 pounds and the allowable 
pressure on the bearing surface is 650 pounds per square inch. 
What is the diameter? 

W = - f 2 X W, and 32,000 = X 650. 

4 4 

t r 

Then __— = the area — 49.23 square inches. 

and d — 7.9 inches. 

An 8 inch shaft would be used. 

In cases where the speed is not very high we may use the fol¬ 
lowing as maximum values of w: 

Wrought iron on gun metal 700 pounds 

Cast iron on gun metal 470 pounds 

Wrought iron or steel on lignum vitae 1,400 pounds 

For high speeds with iron or steel on lignum vitae bearing, 
when moistened with water, the following formula may be used, 

d = .035 y/W7 

The direction of load for a collar bearing is parallel to the 
axis but the bearing area is formed by a collar or collars on the 
shaft. Fig. 49 shows a journal with one collar and Fig. 50 one 



with several collars. To find the diameter of collars for propeller 
shafts we proceed as follows: 






















































MACHINE DESIGN. 


59 


Let d = diameter of shaft, 

D = diameter of collar, 

N = number of collars, 

w ~ pressure per square inch of projected area, 

W = total load. 

The total load is expressed by the equation, 

W = 1 7T (D 2 — d 2 ) N w. 

Usually w is taken as 50 or 60 pounds for propeller shafts. 
Using iv — 60 the formula becomes, 


W = 7T (D2 _ d 2 ) 15 N, 
W 

15 ttN* 


or (D* — d 2 ) = 
Hence D = y d 2 


15 7T N 


The number of collars is determined by the designer. By 
increasing the number, the diameter, wear and friction are de¬ 
creased ; but if too many collars are used all the thrust may be 
brought on a few of them. The distance between collars is 
sometimes equal to the thickness. But if the encircling rings are 
lined with white metal or are made hollow the distance may be’ 1 
made about twice the thickness. 


EXAMPLES FOR PRACTICE. 

1. What are the proportions of a wrought iron end journal, 

when — — 1.2, the load 1,800 pounds, and safe stress 8,500 
d 

pounds? Ans. l-j 3 ^" X 1 T V'- 

2. Find the length and diameter of an end journal when S 
= 9,000 pounds, W == 8,000 pounds and w — 800 pounds. 

Ans. 8f 3 " X 2f" 

8. Find the proportions of a neck journal, if the load is 
7,000 pounds, the bearing pressure 400 pounds and safe stress 
9,000 pounds. Ans. 2^" X 81". 

4. Find the proportions of a neck journal if the load is 

6,000 pounds, the safe stress 8,500 pounds and J— = 1.75. 

d 

Ans. X 2J/. 







60 


MACHINE DESIGN. 


5. Find the power used in friction when the load is 6,000 
pounds, the diameter of the shaft 2 inches, and making 150 revolu¬ 
tions per minute. The coefficient being .002. 

Ans. 942.48 foot-pounds per minute. 

6 . Find the diameter of a wrought iron pivot running at 90 

revolutions per minute, with a load of 850 pounds, having gun 
metal bearings. Ans. li inch shaft. 

7. Find the diameter of the collars on an 8 inch shaft, the 
end thrusts being 18,000 pounds. There are four collars. 

Ans. 12.6 inches. Use 12J inches. 

SHAFTS. 

Shafts are parts of machines which support rotating pieces. 
They are usually circular in section. 

Shafts may be divided into three classes. The classification 
being determined by the kind of stresses to which they are 
subjected. 

1. Shafts subjected chiefly to torsion or twisting. For 
example, shafting used to transmit power, called line shafting. 

2. Shafts subjected chiefly to bending; shafts of gearing ' 
example. 

8 . Shafts subjected to both torsion and bending, as engine 
shafts. 

Shafts of the first class, those subjected to torsion, must be 
designed for both strength and stiffness. If a shaft is of large 
diameter or if it is short it may be designed for strength only; but 
for a long shaft of small diameter, sufficient strength may not 
insure sufficient stiffness. Line shafting is the name given to the 
long continuous lines of shafting used in mills, factories, etc. 
Numerous pulleys are keyed to the shafts from which power is 
taken by belts and gears. These shafts are strained by twisting 
stresses and also by a slight bending action due to the weight and 
the downward pull of the gearing. 

Calculations for size are made by investigating the twisting 
moment which is equal to the force or pull multiplied by the 
radius. 



MACHINE DESIGN. 


61 


t rom the study of “ Mechanics” we know that the diameter of 
a round shaft may he found from the formula: 



in which d = the diameter in inches, 

H z= the horse-power transmitted, 
n = the number of revolutions per minute, 
and S s the constant of torsion and is: 

2,000 pounds per square inch, for timber. 

25,000 pounds per square inch, for cast iron. 

80,000 pounds per square inch, for wrought iron. 

75,000 pounds per square inch, for steel. 

Another formula for ordinary wrought iron mill shafting, is: 


d 




H 

n~X .01153 


The following table has been computed from this formula; 
by multiplying the second column by the number of revolutions 
per minute, the result is the power the shaft will transmit. 


Diameter 
of Shaft 
in inches. 

H. P. 

Diameter 
of Shaft 
in inches. 

H. P. 

n 

n 

If 

0.0623 

5 

1.4536 

2 

0.0930 


1.9344 


0.1325 

6 

2.5112 

21 

0.1817 


3.1944 

2 f 

0.2418 

7 

3.9888 

3 

0.3139 

H 

4.9056 

8 J 

0.3993 

8 

5.9536 

H 

0.4986 

H 

7.1440 

3f 

0.6132 

9 

8.4800 

4 

0.7442 

10 

11.6288 

4f 

0.893Q 

11 

15.4752 

41 

1.0600 

12 

20.0896 

4f 

1.2470 




Hollow Shafts. The inner fibres of a shaft, that is, those 
near the centre are not as useful to resist torsion as the outer. 
Therefore, in making a shaft hollow considerable weight is removed 
and the strength is but little impaired. In other words, if a shaft 
is made hollow its weight is decreased in a greater measure than 





















62 


MACHINE DESIGN. 


its strength. A hollow shaft is much stronger than a solid one of 
the same weight. For marine work hollow shafts are especially 
valuable on account of their light weight. 

Let D = the outside diameter of the hollow shaft. 

d — the diameter of a solid shaft having the same 
strength as the hollow shaft. 

Dj = the inside diameter of the hollow shaft. 

From a mathematical consideration of moments and stresses 
the following formula is deduced: 



Suppose we wish to find the diameter of a hollow shaft which 
shall have the same strength as a solid shaft of nine inches diam¬ 
eter, the internal diameter to be ^ the external. 




= 9 X 1.022 = 9.198 inches. 


The shaft may be made 9^ inches in outside diameter and 
4^| in inside diameter. 

The distance between bearings depends upon the number of 
pulleys on the shaft. If the shaft has several pulleys keyed to it 
the bearings must be nearer than if there are only a few pulleys. 
Large pulleys and those giving out a large amount of power should 
be placed near the bearings. The distance should be such that 
the deflection can not be more than yj-g of an inch per foot. 

The following table gives maximum distance between bear¬ 
ings for shafts of various sizes. 









MACHINE DESIGN. 


63 


Diameter 
of Shaft 

Distance between Bear¬ 
ings in Feet. 

in inches. 

Wrought 
Iron Shafts. 

Steel 

Shafts. 

2 

15.46 

15.89 

3 

17.70 

18.19 

4 

19.48 

20.02 

5 

20.99 

21.57 

6 

22.30 

22.92 

7 

23.48 

24.13 

8 

24.55 

25.23 

9 

25.53 

26.24 


SHAFT COUPLINGS. 

Since it would be inconvenient to manufacture shafts long 
enough for a large factory, some means must be provided to join 
short lengths together. 

Shafting is usually made in lengths of 20 to 30 feet, and 
joined by shaft couplings. These couplings should be placed near 
bearings and on the side farthest from the power. If this is done 
the running part is supported even if a length is disconnected. 

Couplings are made in various shapes according to the posi¬ 
tions of the shafts to be joined. They may be designed for shafts 
having a common axis of rotation, that is, in line; for parallel 
shafts ; or for shafts whose axes intersect. 

Shaft couplings are usually divided into three classes. 

1. Mixed or permanent couplings, which can be discon¬ 
nected only by slacking keys or by removing nuts. 

2. Loose or disengaging couplings, which are provided with 
arrangements for throwing a part of the shafting out of gear with 
slight effort. 

3. Friction Couplings which are loose and so arranged that 
they put the shafting into gear gradually and slip if the resistance 
is great. 

The simplest form of shaft coupling is the box or muff shown 
in Fig. 51. A short iron cylinder is fitted over the ends of the 
shafts. Relative rotation is prevented by a wrought iron key 
which is usually half in the shaft and half in the coupling. The 















64 


MACHINE DESIGN. 


shafts may be enlarged at the ends so that there will be no 
decrease in strength because of the key way. Couplings are 



designed from empirical formulas and not from calculations for 
strength. In Fig. 51 d — the diameter of the shaft, and is 
taken as the unit. 

The dimensions may be calculated from the formulas, 

l = 2ld+2' 
and t = .45 d -f- 1". 

For the key, 

b = {d 

t = \d. 

For example. Find the dimensions for a box coupling for a 
shaft 3 inches in diameter. 

I = a 21 x 3) + 2" = 91 inches 
t — .45 d -j- 1" = 1.85 or 1| inches. 

The key would be, 

b — 4 inch 
t — 1 inch. 

The coupling shown in Fig. 52 is called the clamp coupling. 
It is made of cast iron, is easily removed, has no projecting parts 



Fig. 52. 

and on account of its cylindrical shape can be used as a pulley. 
The faces of the joint are first planed then the holes are drilled. 
































MACHINE DESIGN. 


65 


It is bored out after the two halves are bolted together with paper 
between them. When the paper is removed a slight space is left 
between the halves so that the coupling grips the shaft when the 
parts are bolted together. The key is straight and fits only at the 
sides so that it will not exert bursting pressure on the coupling. 
The following formulas may be used in finding the proportions; 
d being the unit. 

D = 2i d + \" 
l = 3 to 4 d. 

llie bolts may be -| inch in diameter for shafts under 2J 
inches in diameter and ^ or ^ inch for larger shafts. Usually 
four bolts are used for small and six bolts for large shafts. 

Find the dimensions for a clamp coupling for a 3|- inch 
shaft. 

I) == 2|- d -f- Y = 9J- inches. 

I — 3 d — lOi- inches. 

We can use 6 bolts of inch. 

•The flange coupling is shown in Fig. 53. The cast iron 



flanges are keyed to the ends of the shafts to be connected. The 
flanges are then brought face to face and bolted together. Some¬ 
times the flanges are faced in a lathe to insure a good joint. One 
flange is often made to enter the other, as shown in the figure, to 
prevent the shafts from getting out of line. As in the other shaft 
































60 


MACHINE DESIGN. 


couplings, the ends of the shrifts may he enlarged for the key way. 
For designing, d — the diameter of the shaft, which is taken as 
the unit. 

I) =2 1 d+ 2" 

1 = 2d. 

Number of bolts, n , = 3 -\- ( the nearest whole number.) 

rfi = - + V 

n 

o'= H+r- 

Propeller shaft coupling. The coupling shown in Fig. 54 is 



usea for propeller shafts. In this case the hollow steel shaft is 
flanged at the ends and joined by bolts. Let d = the diameter of 
an equivalent solid shaft. Then, 

d =(/5EW 

' D 


The number of bolts is usually 
assumed, and the diameter d v can be computed by a consideration of 
the twisting moment of the shaft and the shearing strength of 
the bolts. 


D 2 = If d 
A ~ 2 d 

= d_ 
e ~2 

The bolts are made tapered. 













































MACHINE DESIGN. 67 


Let n = the number of bolts, and a a constant; then d 1 =ad. 
The values of a for different values of n are as follows : 


n = 3 

1 4 

1 5 

1 6 

1 1 I. § 

1 9 

1 19 

a = .318 

| .283 

| .258 

| .239 

[ .224 | .212 

I .201 

| .192 


h ind the dimensions of a shaft coupling for a hollow pro¬ 
peller shaft 4 inches in external diameter and 2 inches in internal 
diameter using 8 bolts. 


3 /44 _ 04 

d — y- - — = 3.915 inches. 

D 2 = If X 3.915 = 6|- inches (about). 

A = 8 inches (about). 
e = 2 inches (about). 
d x = .212 X 3.915 = if. 

Bolts f inch in diameter would be used. 

Sellars Cone Coupling. A convenient coupling for shafts of 
equal or unequal size is shown in Fig. 55. It consists of an outer 



Fig. 55. 


cylindrical box or muff which is turned of double conical form on 
the inside. Two sleeves, the exterior of which are conical and fit 
the conical surfaces of the box, are placed between the box and 
the shaft. The inside surfaces of the sleeves fit the shaft. Three 
square bolts parallel to the shaft and resting in slots cut in the 
sleeves, press them together. The sleeves are cut through on one 
side at the bottom of one of the bolt slots. This gives sufficient 
elasticity so that the sleeves may be drawn inward and grasp 
the shaft tightly. Each sleeve exerts the same force on the shaft 
and with the aid of a key prevents slipping. The keys fit at the 







































68 


MACHINE DESIGN. 


sides only. These couplings are easily disconnected if the parts 
are well oiled before they are put together. The dimensions may 
be found from the following formulas : 


D 

l 

b 

a 

size of bolts d 1 
In the above formulas 


= 3 
= 4 


— d 

= \d 


= ¥ 

d is the unit, and is taken as the 
diameter of the shaft. The conical sleeves have a taper of about 
4 inches per foot of length. 

The Oldham Coupling. Fig. 56 shows a form of coupling 
used when two shafts are parallel. A disc is keyed on the end 
of each shaft. Between these discs lies a third which has a 



f -5!- * 

'K 



b 

t 


u_j 

1 

s 



■«1— c — * 

#—e—Xj 

X 

: j- 



mJ 


Fig. 56. 

feather on each side fitting in a slot in the corresponding disc. 
The middle disc revolves around an axis parallel to the shafts and 
midway between them. The shafts and disc have equal velocities. 

The proportions for this coupling may be as follows: 
d — diameter of shaft, 
a = Ad , 
b = 1.75 d, 
c — .8 d, 

e = .7 d, 
i = .25 d, 
t= 3 d. 





















MACHINE DESIGN. 


69 


The Universal Coupling. In case two shafts are not in line 
they may be connected by a universal coupling shown in Fig. 57. 



Fig. 57 


The velocity ratio varies but little if the angle is small. They 
are constructed of wrought iron and may have the following pro¬ 
portions ; d being the unit. 

d — diameter of the shaft, 
a — d to 2 d, 
b — If d, 
e = If d, 
e =\d, 

9 = 2tf, 

h = | d. 

Loose Couplings are used if shafts are to be connected and 
disconnected. A type called a claw' coupling which somewhat 
resembles the flange coupling is shown in Fig. 58. It is used for 
large slow turning shafts, which always revolve in the same direc¬ 
tion. This form is easily put in gear. In place of the flanges 
there is a set of projections or lugs which fit into recesses. One 
part is firmly keyed to the shaft by a sunk key; the other is 
fastened by a feather key. The part having the feather key (on 
the left hand) is prolonged and a groove cut for a lever with 
which to slide it back and forth. 




























TO 


MACHINE DESIGN. 


A coupling which is easily put in gear hut can drive only in 
one direction has its claws shaped as shown in Fig. 59. 




The dimensions may be as follows: 

d — diameter of shaft, 

a =i d, 
o = §d, 
e — "4 d, 
i = 1 J d, 
l = l i d to 6 d. 



Friction Couplings, or clutches serve instead of loose coup* 










































MACHINE DESIGN. 


71 


lings on shafts running at high speeds. Fig. GO shows a good 
form of friction clutch. The ring, g, is keyed to the shaft t. 
This ring is split and fits inside the cylinder c, which is keyed to 
the shaft i. Ihe split ends are connected by a screw having 



right and left hand threads. The link d, connects the lever b, to 
the sleeve or collar a. The lever 5, turns the screw. The clutch 
is readily operated. When the sleeve is pushed toward the cylin¬ 
der c, the rotation of the screw throws the ends h of the ring 
apart, and causes the ring e to press firmly against the cylinder c. 

The proportions for the various parts are about the same as 
those for Fig. 58. The clutch shown in Fig. 62 is not as good as 
that of Fig. 60 because it causes an end thrust on the shaft and it 
is harder to put in gear. It is, however, simple in construction. 

Weston Friction Coupling. The friction coupling shown in 
Fig. 61 is used both as a shaft coupling and for coupling a spur 



wheel to a shaft. The wheel B has a long hub and wrought iron 
rings or plates which slide on feathers. The clutch box A is fitted 
on the shaft, slides on feathers, and is moved by a lever working in 















































72 


MACHINE DESIGN. 


the groove E. Inside the box A are six feathers upon which are 
strung alternately wooden and wrought iron rings. If the coup¬ 
ling box A is pressed to the left there is friction at each face 
between the rings. The wheel B is prevented from moving end¬ 
wise by the collar C. One of the great advantages of this coup¬ 
ling is that if a sudden load comes on the spur wheel B, the plates 
merely slip over each other; if rigidly connected, some part 
would break. 

Fig. 62 shows a simple form of friction coupling or clutch. 
It is used to couple wheels or pulleys to shafts and for loose 



couplings for shafts running at high speeds. It consists of a cone 
keyed rigidly to one shaft and a movable cone sliding on a feather 
on a second shaft. The movable portion should be placed on the 
driven shaft so that it will be at rest when out of gear. If the 
resistance of the driven shaft is considerable the mean cone radius 
may be three or four times the diameter of the shaft. One great 
objection to this form is that the horizontal component of the 
pressure between the conical surfaces causes end thrust on the 










































MACHINE DESIGN. 


73 


shaft. The angle of the cone may be from 4 to 10 degrees. The 
other proportions are as follows: 

a — diameter of shaft, 
b = If a, 
c = 1| a, 
d — 2 a, 

A = 4a to 8a, 
i — i a i 

t = 2 a. 

Shifting Gear for Clutches. Forked levers, having prongs 
which fit into the groove of the clutch, are used to put clutches in 




and out of gear. The lever is ordinarily worked by hand. Some¬ 
times a brass strap is made to encircle the groove; this increases 
the wearing surface. The following dimensions refer to Fig. 63 ; 
the unit being the diameter of the shaft. 

a = the diameter of the shaft, 
a = T 5 g <?, 
b = $e 9 


i 






















EXAMINATION PAPER. 


MACHINE DESIGN PART I. 




L, «f c. 


MACHINE DESIGN 


Instructions to the Student. Place your name and full address at the 
head of the paper. Work out in full the examples and problems, showing each 
step in the work. Mark your answers plainly u Ans.” Avoid crowding your 
work as it leads to errors and shows bad taste. Any cheap, light paper like 
the sample previously sent you may be used. After completing the work add 
and sign the following statement. 

I hereby certify that the above work is entirely my own. 

(Signed) 


1. A wheel 42 inches in diameter makes 35 revolutions per 

minute. What is the linear velocity of a point on the circumfer¬ 
ence? Ans. 6.4 feet per second. 

2. If the angular velocity of a wheel 6 feet in diameter is 30 
per second, what is the linear velocity ? Ans. 90 feet per second. 

3. Define reciprocating motion, continuous motion, and 
intermittent motion. 

4. What is a machine? 

5. Why are the relative movements of the parts of a 
machine independent both of the power transmitted and the size 
of the parts ? 

6. Define power and its unit. 

7. Why are not foot-pounds an indication of Horse-Power? 

8. Name some forms in which potential energy may exist. 

9. What is the energy of a body weighing 20 pounds and 
moving with a velocity of 4 feet per second ? 

Ans. 4.97 foot-pounds. 

10. In designing an engine why would you make the piston 
rod of wrought iron or steel rather than of cast iron ? 

11. Explain with sketch why all corners of castings should 
be well rounded. 

12. Why are castings weak if some parts are much heavier 
than others ? 

13. What elements and processes are employed to get sound 
steel castings ? 




MACHINE DESIGN. 


14. Name tlie principal strains in machines and the methods 
used in designing to allow for these strains. 

15. What metals are used for hearing alloys? 

16. If you were making a working drawing of an engine 
crank, how many views would you make ? 

17. When are sectional views used? 

18. Which is the best method of designing, by theory, or 
practice, or by a consideration of both ? 

19. Name some part of a machine that is designed from cal¬ 
culation for strength. Some part designed to provide for wear. 

20. Describe with sketch the standard U. S. screw or bolt 
thread. 

21. What is the safe working stress on a bolt if the diame¬ 
ter is 1^ inches and the load 8,800 pounds? Ans. 4,2<3 pounds. 

22. Why are multiple threads used when motion is to be 
transmitted ? 

23. Describe the standard bolt and nut. 

24. Why is the Sellars thread not suited for gas pipe ? 

25. An engine cylinder-head is bolted to the cylinder with 

8 bolts. If the maximum total steam pressure on the piston is 
28,000 pounds, what is the diameter of the bolts ? Assume safe 
working stress as 5,000 pounds. Ans. 1^ inches in diameter. 

26. What is the pitch of a screw? 

27. If a bolt is 11 inches in external diameter, what is the 

pitch? Find by formula. Ans. .185 inches. 

28. Describe the Whitworth thread. 

29. When are taper threads used ? What is the advantage 
of the buttress thread ? 

30. Describe with sketch some method of fastening founda¬ 
tion bolts. 

31. What is a key? 

32. Describe the knuckle joint. 

33. Is the Grover’s spring a good locking device ? Why? 

34. Describe with sketch what you consider a good locking 
arrangement for nuts. 

35. When are pin keys used ? 

36. Describe the method of fastening small engine cranks 
on shafts. 





MACHINE DESIGN. 


79 


37. Why are keys tapered ? About how much is the taper? 

38. What is the most effective form of key? Why? 

39. Find the length of a steel key which is an inch wide 

when a 3 inch shaft transmits 50 hcrse-power at 100 revolutions 
per minute. 4ns. 3 inches. 

40. Find the dimensions ot a cottei and rod of the form 
shown in Fig. 42. The load being 5,500 pounds and S t = 7,000 
pounds. 

(d = 1| inches 
1^=1 inch 
| d 2 = ly 6 inches 
Ans. ^ I) — 2.1 inches 
t = inch 
b — l^g inches 
^ a = to l T 9 g inches. 

41. Make a sketch of a locking device for a cotter that lias 
considerable taper. 

42. A cotter is 2 inches wide at one end and 2|- at the other. 
If it is 14 inches long what is the taper per foot? 

A ns. | inch per foot. 
43 Find the length and diameter of a steel end journal when 

Che load is 2,300 pounds. Assume ~ = 1.75 and the safe work- 

d 

ing stress S, as 8,500 pounds. Ans. ly 9 g in. diam. and 2-| in. long. 

44. Find the proportions of a steel end journal when the 

load is 10,000 pounds, the safe working stress 9,000 pounds, and 
the allowable pressure 850 pounds. Ans. 2-| X 4£ inches. 

45. Find the diameter and length of a wrought iron neck 

journal when W = 5,000, S = 7,500 and L. = 2. 

Ans. ly 5 ^ in. diam. and 2| in. long. 

46. What is the height and breadth of collar for the above 

journal ? Ans. in. in height and | in. in breadth. 

47. What is the diameter of a pivot journal when the load 

is 25,000 pounds and the allowable pressure is 600 pounds per 
square inch? Ans. 7f inches. 

48. The end thrust on a 9 inch shaft is 12,000 pounds. 
Find the diameter of the collars assuming 5 are used. 

Ans. D = lli inches. 




80 


MACHINE DESIGN. 


49. What is the diameter of a mill shaft which transmits 55 

horse-power at 90 revolutions per minute? Ans. 3i| inches. 

50. Why is a hollow shaft stronger than a solid one of equal 
weight ? 

51. Find the outside and inside diameters of a hollow shaft 
that equals in strength a solid shaft 8 inches in diameter. The 
inside diameter to he J the outside. Ans. 8^ and 4^ inches. 

52. Why is the distance between bearings small ? 

53. Describe with sketch a good simple shaft coupling. 

54. Draw a sketch and calculate the dimensions of a clamp 
coupling like that shown in Fig. 52. The shaft being 4 inches 
in diameter. 

OPTIONAL 

For students taking Hechanical Drawing. 

Assume convenient scale. 

1. Design and draw a knuckle joint having d = 2 inches. 

2. Design and make two sectional views of a cotter like the 
one shown in Fig. 42. Assume d — 1| inches. 

3. Make a drawing of some form of shaft coupling for a 3 
inch shaft. 

4. Design and make the drawings of a friction coupling for 
a 3| inch shaft. 

5. Design and draw a Sellar’s Cone coupling for a 2^ inch 
shaft. Two views. 






























V 






* 






* 






* 














